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Development of back-end processing system for high frequency ultrasound b-mode imaging
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Development of back-end processing system for high frequency ultrasound b-mode imaging
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Content
DEVELOPMENT OF BACK-END PROCESSING SYSTEM
FOR HIGH FREQUENCY ULTRASOUND B-MODE IMAGING
by
Jin Ho Chang
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)
December 2007
Copyright 2007 Jin Ho Chang
ii
DEDICATION
With grateful thanks to my adored parents, Cheol-Hee Chang and Yang-Soon Kim;
my beloved wife, Ji Sun Kim;
my precious son, Hyoun Wook Chang
for their unconditional love and unflagging support
iii
ACKNOWLEDGEMENTS
It is my pleasure that I have been able to have countless opportunities making
for a full and enriching experience during my stay here at the University of Southern
California. Without the truly special people I have met for the past four years, I could
not have enjoyed my research and accomplished this dissertation.
I would like to first thank my advisor, Dr. K. Kirk Shung. He provided the
special opportunities and let me freely carry out my research with his support and
encouragement. I would also like to thank Dr. Jesse T. Yen for his valuable
suggestions when I designed the system presented in this work. My thanks also go to
Dr. Jonathan M. Cannata, Dr. Ellis Meng, and Dr. Eun Sok Kim for their precious
advices on this dissertation. In addition, I have to express my appreciation to all my
colleagues at the NIH Resource Center for Medical Ultrasonic Transducer
Technology for their friendship as well as discussion on my research. Dr. Jung Woo
Lee, Mr. Hyung Ham Kim, and Mr. Jong Seob Jeong, particularly, deserve my
special thanks. They have made my life enjoyable as great mentors and friends.
With all my heart, I would like to thank my lovely family, in particular my
adored parents for their devotion and unflagging prayer for me throughout my life.
My brother, Min Ho, and my sister, Eun Kyoung, have been always supportive and
made me feel their love. Also, I must thank my beloved wife, Ji Sun, and my
precious son, Hyoun Wook, for their endless love. They have always given me their
unquestioning faith and encouraged me to keep moving forward to my dream. I
would like to dedicate this dissertation to you all with my love.
iv
TABLE OF CONTENTS
DEDICATION ………………...………………...………………………………….......ii.
ACKNOWLEDGEMENTS ………………...………..……………………………….......iii.
LIST OF TABLES ………………...……………………………………………….......vi.
LIST OF FIGURES ….……………….…………………….………………………….vii.
ABSTRACT ……………………………………………………………………….….xii.
CHAPTER 1. INTRODUCTION ……..……...………………..............................…….…..1.
1.1 General ………………...……………………………….....................................1.
1.2 High Frequency Ultrasound Imaging ……………………………………….....4.
1.3 High Frequency Ultrasound Scanning Methods ……………………………….7.
1.4 Objective of Research …………………...……………………………………11.
1.5 Overview ……………………………………………………………………...13.
CHAPTER 2. BACK-END PROCESSING IN ULTRASOUND B-MMODE IMAGING SYSTEM 15.
2.1 General …...……………………………………………...................................15.
2.2 Envelope Detector …………………………………………………………....19.
2.2.1 Ideal Hilbert Transformer ………………………………………………21.
2.2.2 Rectification of RF Signal Followed by Filter …………………………22.
2.2.3 Approximate Hilbert Transformer ……………………………………...25.
2.2.4 Quadrature Demodulation ……………………………………………...28.
2.3 Logarithmic Compressor ………………………………………………….….31.
2.4 Digital Scan Converter (DSC) …..……………………………………………34.
2.4.1 Accuracy of Linear Interpolation ……………………………………….37.
2.5 System Requirements for High Frequency Ultrasound Imaging ……………..45.
CHAPTER 3. A NOVEL ENVELOPE DETECTOR FOR HIGH FRAME RATE,
HIGH FREQUENCY ULTRASOUND IMAGING ……………………..…...…48.
3.1 Introduction ……...……………………………………….……….………..…48.
3.2 Description of Proposed Design ……………………………………………...52.
3.3 Experimental Results ….………………………………………….…..………60.
v
3.4 Conclusions …………………………………………….…………………….65.
CHAPTER 4. DESIGN OF HIGH FRAME RATE DIGITAL SCAN CONVERTER
FOR HIGH FREQUENCY ULTRASOUND SECTOR SCANNER …….….….…68.
4.1 Introduction ……...………………………………………………………....…68.
4.2 Overview of DSC Work Flow ………………………………………………..71.
4.3 System Description …………………………………………………………...75.
4.3.1 Pixel Address Generator ………………………………………………..76.
4.3.2 Coordinate Transformer and Interpolator ………………………………82.
CHAPTER 5. HIGH SPEED BACK-END PROCESSING SYSTEM
FOR MECHANICAL SECTOR SCANNER ……..……...….…………...........85.
5.1 Mechanical Sector Scanner ……………………………………………….......85.
5.2 Back-end Processing System for B-Mode Imaging ……..……………………87.
5.2.1 DC Canceller …….……………………………………………………..90.
5.2.2 Digital Time Gain Compensator ………………………………………..92.
5.2.3 PCI Bus Controller ……………………………………………………..96.
5.2.4 User Interface Module ………………………………………………….99.
5.3 Experimental Results ………………………………………………………..102.
5.3.1 Processing Speed ……………………………………………………...105.
5.3.2 Image Quality …………………………………………………………108.
5.4 Conclusion …………………………………………………………………..115.
CHAPTER 6. SUMMARY AND FUTURE WORK …………………….…………..…….117.
6.1 Summary …....……..………………………………………………………...117.
6.2 Future Work …………………………………….…………………………...119.
6.2.1 Coded Excitation for Improving SNR ………………………………...120.
6.2.2 Frequency Compounding by Using Dual Element Transducers ……...121.
BIBLIOGRAPHY …………………………………………………………….…........126.
Appendix A ………………………………………………………………………..135.
vi
LIST OF TABLES
Table 2-1: Summary of the normalized RMSE values of the envelope detection
algorithms ............................................................................................30.
Table 2-2: Comparison of accuracy of the linear interpolation and the bilinear
interpolation algorithms by computer simulation using Field II
program …………………………………………………………...….39.
Table 2-3: Summary of system requirements for high frequency ultrasound
B-mode imaging ……………………………………………………..47.
Table 5-1: Parameters of the single element transducers used in the
experiments ………………………………………………………....102.
vii
LIST OF FIGURES
Figure 1-1: Conceptual diagram of electrical scanning ……..…………....……….8.
Figure 1-2: Conceptual diagram of mechanical scanning ...……….………….....11.
Figure 2-1: Block diagram of generic ultrasound imaging system ………………16.
Figure 2-2: Echo signal used in simulation to examine the levels of accuracy of
envelope detection algorithms ………………………………………20.
Figure 2-3: Accuracy of the envelope information extracted by the rectifier with
a median filter and the rectifier with LPF …………………………...24.
Figure 2-4: Block diagram of envelope detectors realized by the Hilbert filter
method and the time delay method ……………….…………………26.
Figure 2-5: Accuracy of the envelope information extracted by the time delay
method and the Hilbert filter method ……………….……………….27.
Figure 2-6: Block diagram of the envelope detector realized by the quadrature
demodulation method ……………………………………………….28.
Figure 2-7: Accuracy of the envelope information extracted by the quadrature
demodulation compared with the outcome from the Hilbert filtering
and the ideal Hilbert transforming …………………………………..29.
Figure 2-8: Logarithmic compression characteristic plot
along different dynamic range (DR) ………………………………...32.
Figure 2-9: An implementation example of logarithmic compressors
for fast update of parameters ………..………………………………33.
viii
Figure 2-10: Conceptual representation of bilinear and linear interpolation ……...36.
Figure 2-11: Point target images obtained when a sampling rate is 40 MHz (
max
2 f )
and the pixel-to-pixel space is 18.5 m μ ……………………………..41.
Figure 2-12: Lateral beam profiles of three point targets shown in Figure 2-11 ….42.
Figure 2-13: Point target images obtained when a sampling rate is 100 MHz (
max
5 f )
and the pixel-to-pixel space is 18.5 m μ ……………………………..43.
Figure 2-14: Lateral beam profiles of three point targets shown in Figure 2-13 ….44.
Figure 3-1: Conceptual block diagram of the proposed design ………………….56.
Figure 3-2: Hardware logic description to extract the logarithmic-compressed
envelope information from the baseband components represented
by a m-bit fixed-point number system ………………………………57.
Figure 3-3: Comparison of accuracy of the proposed design
with that of the conventional quadrature demodulation method ……61.
Figure 3-4: Logarithmic-compressed envelope information extracted
by the proposed design implemented in FPGA ……………………..63.
Figure 3-5: B-mode image of the excised pig eyeball
involving the proposed design ………………………………………66.
Figure 3-6: B-mode image of the excised pig eyeball
involving the ideal Hilbert transformer ……………………………..67.
Figure 4-1: Configuration of pixel addressing of 256 by 256 sized image ……...72.
ix
Figure 4-2: Sector scanning slice colored gray formed
by two adjacent scanlines …………………………………………...73.
Figure 4-3: Timing diagram describing DSC work flow
when the number of scanlines is 8 as an example ………………….74.
Figure 4-4: Functional block diagram of designed digital scan converter ………76.
Figure 4-5: Description of grouping effective pixels and linear interpolation
within two adjacent scanlines ……………………………………….78.
Figure 4-6: An example to describe the contents of LUT and its output value …..80.
Figure 4-7: Hardware logic description of a pixel address generator (PAG) ........81.
Figure 4-8: Flow chart to explain the functionality of PAG ………...…………...82.
Figure 5-1: Functional block diagram of a front-end system of
a mechanical sector scanner …………………………………………86.
Figure 5-2: Scheme of generating PRF trigger signals based on
a given motor position signal from the servo motor controller ……..86.
Figure 5-3: Overall system block diagram of designed back-end processing
system for B-mode imaging …………………………………………88.
Figure 5-4: Result of a DC canceller implemented using a high pass filter ……..91.
Figure 5-5: Hardware logic description of
the digital time gain compensator implemented in this work ……….93.
x
Figure 5-6: Results of verifying the functionality of
the implemented digital time gain compensator …………………….94.
Figure 5-7: Effect of DTGC on the A-line samples
after the DC canceller shown in Figure 5-4 ………………………....95.
Figure 5-8: Block diagram of PCI bus controller employing master mode PCI
operation with direct memory acess (DMA) method ……………….97.
Figure 5-9: Graphic user interface (GUI) ………………………………………100.
Figure 5-10: Flow chart of the user interface module …………………………...101.
Figure 5-11: Pulse-echo responses and frequency spectrums of the 40-MHz
single element transducers used in the experiments ……………….103.
Figure 5-12: Experiment arrangement ……………………………...……………104.
Figure 5-13: Image obtained by the scan conversion with four-cycle 25-MHz
sinusoidal burst signals created by a function generator …………..105.
Figure 5-14: Images of a rotating stir bar with their time stamps .………………107.
Figure 5-15: Photograph and schematic of a wire phantom ….….………………108.
Figure 5-16: Wire phantom image obtained using the type B transducer ……….109.
Figure 5-17: The beam profiles of the third wire image shown in Figure 5-16 …111.
Figure 5-18: Image of the anterior segment of a pig eye obtained in vitro ……...112.
xi
Figure 5-19: Pig eye image illustrating the sclera commonly known as
the white of the eye, cornea join forming anterior chamber angle,
zonular fibers located behind the iris, and the ciliary body ………..113.
Figure 5-20: Photograph of the setup for in vivo mouse heart imaging …………114.
Figure 5-21: Still images of moving the mouse heart acquired
at the rate of 67 images per second ………………………………...116.
Figure 6-1: Transmit signals and their frequency spectrums
generated from a dual element transducer ………………………....124.
Figure 6-2: Echo signals from the posterior segment of a pig eye,
which were received by the outer (top panel) and
the inner (bottom panel) annuli ………………….…….…………...125.
Figure A-1: Anatomy of the human eye ………………………………………...135.
Figure A-2: Different cross sectional view of the heart
depending on scanning direction …………………………………..136.
xii
ABSTRACT
High frequency ultrasound is capable of providing fine spatial resolution on the
order of several tens of micrometers and fine temporal resolution of more than 200
frames per second. These capabilities are applicable to the cardiac imaging of the
mouse where the heart rate is 5-10 beats per second. In order to adequately capture
the cardiac activity of the mouse, two key elements are required: high-speed
acquisition of echo signals (front-end system) and high-speed signal processing
functions to extract clinically useful information from the acquired echo signals and
to display the information on a monitor in real time (back-end system).
This thesis presents the development of a high speed back-end processing
system for high frequency ultrasound B-mode imaging, which requires a very fast
computational speed and a very wide bandwidth of data transfer between each
functional block. In order to achieve the requirement, a DC canceller, a digital time
gain compensator, a novel envelope detector with capability of logarithmic
compression, and a digital scan converter (DSC) capable of performing fast
coordinate transformation and data interpolation are proposed. In addition, the wide
bandwidth of data transfer between the DSC module and an image display module is
achieved by using a 64-bit 33 MHz PCI bus.
The operating speed of the developed back-end system was examined by
recording the completion time of transferring an image to PC and by acquiring
xiii
images of a moving object at predetermined speed. Through these experiments, it is
shown that the back-end system developed is capable of acquiring up to 400 images
consisting of 256-by-256 pixels per second at 100 MHz system clock frequency. At
present, its display rate is 95 images per second due to the limitation of a monitor’s
capability although one thousand scan converted images can be stored in the hard
disk of PC. By wire phantom, in vitro pig eye, and in vivo mouse heart imaging
experiments, it is verified that the developed system is capable of serving as a back-
end processing system to maximize benefits of high frequency ultrasound, i.e., a fine
spatial and a fine temporal resolution.
1
CHAPTER 1
INTRODUCTION
1.1 General
As a real time medical imaging modality, ultrasound imaging systems have
been used for obstetric, cardiac, carotid artery, and prostate imaging providing a
wealth of information for noninvasive or minimal invasive diagnosis. The range of
center frequency of transducers used for conventional medical imaging is from 2
MHz to 10 MHz, and the spatial resolution of an ultrasound image is on the order of
a few millimeters. The range of maximum imaging depth is from 40 mm to 240 mm
depending on the center frequency of transducers used, and the frame rate
corresponding to temporal resolution is typically 30 images per second for normal
organ imaging or up to 70 images per second for cardiac imaging with decreasing
image size (Sikdar et al., 2003). These specific features are related to the center
frequency of transducers used for imaging either directly or indirectly.
Spatial resolution of an ultrasound image can be divided into three types: axial,
lateral, and elevation resolutions along with each axis. The axial axis is in the beam
propagation direction. The lateral axis is perpendicular to beam direction, so that the
axial and lateral axes define a 2-D ultrasound imaging plane. The elevation axis is
perpendicular direction to the imaging plane. The axial resolution is mainly
2
determined by the center frequency and the bandwidth of a transducer and the lateral
resolution can be improved by increasing the center frequency and/or the aperture
size of a transducer. The lateral and the axial resolutions are calculated through the
following equations:
#
0
f
lateral
Z
c
Rf
fD
λ ≈ ⋅ = ⋅ (1−1)
6
2
axial
dB
c
R
BW
−
=
⋅
(1−2)
where λ is the wavelength defined as the ratio of the sound velocity to the center
frequency of transducers (
0
cf ),
#
f is the f-number defined as the ratio of focal
depth to aperture size (
f
Z D ), and
6dB
BW
−
represents a -6 dB bandwidth of the
transfer function of transducers. A peculiar property of the lateral resolution is that it
degrades with imaging depth like
f
Z in Equation (1-1) due to the diffraction of
ultrasound. Because of this property, the focusing cannot have an effect on image
quality beyond a transition point of the near-field and far-field,
2
a λ , where a
represents the dimension of the aperture. Because of the difficulty in fabricating 2-D
array transducers, 1-D array transducers usually employ a fixed mechanical focus
with relatively high f-number to guarantee a sufficient depth of focus in the elevation
direction (Wildes et al, 1997).
The magnitude of ultrasound traveling in the axial direction exponentially
decreases as a function of depth z as shown in Equation (1-3) in which α is called
ultrasound pressure attenuation coefficient affected by both absorption and scattering
3
of ultrasound energy (Shung, 2005).
( )
0
z
pzpe
α −
= (1−3)
where
0
p is the pressure at zero depth ( ) 0 z = . The attenuation coefficient in tissue
is proportional to the frequency of ultrasound, so that the peak frequency of
transmitted ultrasound is down-shifted as propagation depth is increased. This means
that the attenuation not only causes a decrease of the ultrasound pressure, but it also
degrades the axial resolution with an increase of imaging depth. The attenuation is
the main factor that limits the depth of penetration in an imaging system.
The frame rate of ultrasound imaging systems is determined by the number of
scanlines and maximum imaging depth, which can be expressed as:
2
PRF
SL SL
c f
FR
dN N
== (1−4)
where c is the sound velocity (1540 m/s in soft tissue), d is the maximum imaging
depth,
SL
N is the number of scanlines constituting an image, and
PRF
f is the pulse
repetition frequency determined by a time interval of between two successive firing
events. As seen in Equation (1-4), the frame rate can be increased by reducing the
maximum imaging depth and/or the number of scanlines. It should be noted that the
distance difference between two scanlines should be less than -3 dB main lobe width
of the lateral beam profile to prevent artifacts resulting from undersampling leading
to deteriorating image quality (Hwang et al., 2001). Therefore, it is not a common
remedy for the sake of increasing frame rate by reducing the number of scanlines.
4
1.2 High Frequency Ultrasound Imaging
High frequency ultrasound imaging with 20 MHz to 100 MHz transducers
changes the features mentioned in the previous section. The spatial resolution is
improved to several tens of micrometers, which is among the best in medical
imaging modalities. The improvement of the spatial resolution can be determined
from Equation (1-1) and Equation (1-2) which indicate that the higher the center
frequency of ultrasound, the higher resolution. However, this best spatial resolution
can be achieved only within a smaller imaging depth due to the frequency dependent
attenuation of ultrasound because the attenuation coefficient α in Equation (1-3)
increases with the frequency of ultrasound. Thus, the maximum imaging depth is
approximately 15 mm for 20 MHz transducers and 1 mm for 100 MHz transducers
although the exact values are determined by the attenuation properties of the tissues
to image (Foster et al., 2002; Passmann et al. 1996). Since the maximum imaging
depth is smaller than that of conventional ultrasound imaging, high frequency
ultrasound imaging is capable of providing fine temporal resolution more than 200
images per second by increasing
PRF
f in Equation (1-4).
The new features, that is, a fine spatial and a fine temporal resolution in the
small imaging depth have opened up new applications: ophthalmic, dermatologic,
intravascular, small animal, and molecular imaging. High frequency ultrasound in
the range of 35 MHz to 100 MHz is capable of resolving important clinical structures
of the anterior part of the eye including the anterior chamber, the ciliary body,
5
zonules in which tumors and cysts frequently appear, the iris, and corneal joint which
is important to research on glaucoma (Foster et al., 1993; Passmann et al., 1996). In
addition, it has been shown that a 20 MHz transducer or a dual element transducer
for 20 MHz / 40 MHz harmonic imaging can be used for imaging the posterior
segment of the eye which is clinically important to diagnose pathologies of the
posterior pole such as macular degeneration and detached retina (Coleman et al.,
2004; Kim et al., 2006).
In dermatology, the anatomic distribution, color, configuration, and visible
surface changes of a lesion in the skin are important evidences to diagnose skin
diseases. Ultrasound ranging from 20 MHz to 100 MHz can be used depending on
the purposes of the diagnoses of skin diseases within a particular layer of the skin
(Schmid-Wendtner et al., 2005; Thiboutot, 1999; Vogt et al., 1998; Passmann et al.,
1996). With 20 MHz transducers, preoperative information about the tumor size can
be obtained and the thickness of the skin can be estimated in order to assess aging
process of the skin. 40 MHz and 50 MHz transducers are capable of examining
lesions of psoriasis and psoriatic plaques and providing the visualization of
melanomas. By using 100 MHz transducers with a B-mode and depth (B/D)
scanning method and a synthetic aperture technique, the skin tumors such as
malignant melanoma can be evaluated.
Intravascular imaging is mainly performed by transducers operating in the
frequency range of between 20 MHz and 60 MHz in order to characterize the
mechanical properties of the arterial walls and detect plaque in the vessels.
6
Lockwood et al. (1992) reported the possibility of examining muscular and elastic
arteries with sufficient resolution by using a needle-type transducer in frequency
ranges of 40 MHz to 65 MHz.
Small animals such as the mouse and the zebra fish are powerful models for
genetic engineering such as phenotype discovery and for drug development to treat
human diseases such as cancer. High frequency ultrasound may be a candidate to
monitor and evaluate the development and treatment of diseases in such small
animals because of its fine spatial and temporal resolution. With transducers ranging
from 40 MHz to 60 MHz, mouse early embryonic neural tubes and hearts, mouse
heart motion, the mid-hindbrain deletion associated with a null mutation of the Wnt-1
proto-oncogene, and melanoma growth have been investigated (Turnbull et al., 1995;
Foster et al., 2000; Xu et al., 2005).
High frequency ultrasound imaging system may also be a potential tool for
molecular imaging. It can be used to evaluate cell morphological change caused by
mitosis, necrotic death, and apoptosis because this change leads to a higher level of
ultrasound backscatter signals (Baddour et al., 2005). With very high frequency
ultrasound (over 100 MHz), the mechanical properties of living cells can be
characterized through measuring the speed of sound in tissue, the attenuation of echo
signals along with scanning positions, and the variation of the intensity of echo
signals (Liang and Blomley, 2003).
7
1.3 High Frequency Ultrasound Scanning Methods
In ultrasound imaging systems, two different types of scanning methods are
currently used: electronic scanning and mechanical scanning. Electronic scanning is
a common method used in conventional medical ultrasound imaging systems
utilizing linear, phased, and convex array transducers. Figure 1-1 shows a conceptual
diagram of the electronic scanning classified as linear scanning with linear array
transducers and sector scanning with phased array transducers. In the linear scanning,
a scanline is obtained through a predetermined sub-aperture that consists of active
elements represented by gray boxes in Figure 1-1 (a). The entire image is obtained
by linearly moving the sub-aperture via electronic selection of active elements. In
transmitting, the active elements are excited with time delays in order to focus
ultrasound generated at a fixed focal depth. In receiving, echo signals focused at
desired imaging points are obtained by commonly using delay-sum beamformation
in which arrival time differences of echo signals between the active elements from
the desired imaging points are computed and the echo signals are summed with the
time differences, that is, time delays. On the other hand, the sector scanning is
carried out by using the entire transducer aperture instead of the sub-aperture in the
linear scanning. Each element is excited with time delays taking into account a
transmit-focal depth and steering angles. Receive focusing is performed in the same
way of the linear scanning.
The electronic scanning is capable of offering the best performances in terms
8
of easy use, good lateral resolution, and fast scanning. However, it has been
challenging to say the least to take full advantage of the performances of array
transducers in high frequency ultrasound imaging. One of the challenges is the
design and fabrication of linear and phased array transducers operating a frequency
beyond 30 MHz (Ritter et al., 2002; Cannata et al., 2006). As the center frequency of
(a)
(b)
Figure 1-1: Conceptual diagram of electronic scanning divided into (a) linear
scanning with linear array transducers and (b) sector scanning with phased array
transducers. Gray boxes represent active elements at which transmit and receive
events take place.
9
transducers is pushed higher and higher, for instance, the size of a pitch defined as
the distance between the centers of two elements becomes smaller and smaller due to
the need to suppress grating lobes that severely degrade image quality. This can be
explained by the relationship between the pitch and the angle of grating lobes; the
pitch and the center frequency of an array transducer determine the location in lateral
axis of grating lobes, which can be expressed as:
11
0
sin sin
g
nnc
dfd
λ
φ
−−
⎛⎞
⎛⎞
==
⎜⎟ ⎜⎟
⋅
⎝⎠
⎝⎠
(1−5)
where 1, 2, n=± ± L, and d is the size of a pitch. In order to obtain grating-lobe-
free images, the pitch for phased array transducers should be less than a half λ
although it for linear arrays has the range between 0.75 and 1.5 λ depending on the
size of aperture (Shung, 2005). From this fact, it is obviously seen that high
frequency array transducers should have a very small size of pitch compared to
conventional arrays. In case of 30 MHz array transducers, for example, the pitch
would be 25.7 m μ for a phased array and 38.5 to 77 m μ for a linear array. Using a
conventional fabrication method, that is, a mechanical dicing approach, one will
have elements with a small effective area because of the relatively large size of kerf
defined as the space between two adjacent elements. It causes a low sensitivity of
transducers, that is, a low signal-to-noise ratio (SNR), thus producing poor-quality
images with a narrow dynamic range.
Another challenge is to develop a hardware system for electronic translation
with transmit/receive beamformation. Since high frequency array transducers
10
provide high-frequency and board bandwidth signals, the system has to operate at
high clock rate. This requires high-frequency electronic components that are
relatively expensive or currently unavailable. For example, digital transmit and
receive beamformers for high-frequency phased array transducers need high-speed
analog-to-digital converters (ADC) running at more than
max
8 f for an acceptable
phase error, where
max
f is the highest frequency component of transmit and receive
signals (Ramm and Smith, 1983). For 30 MHz phased arrays, a 12-bit 400 MHz
ADC is at least required, which is commercially not available. In addition, the high
clock rate brings about clock noise in the entire system, which deteriorates the
quality of echo signals. So more sophisticated design of printed circuit board (PCB)
is required in order to alleviate the problem.
Mechanical scanning with single element transducers is the most common
method for high frequency ultrasound imaging because it is relatively easy to build
transducers operating above a frequency of 30 MHz. The mechanical scanning can
be performed in two different ways: straight line scanning and sector scanning as
shown in Figure 1-2. Since stepping or servo motor systems are responsible for
translating the transducer along with an image plane, maximum scanning time
depends on the performance of the motors. Typically, the mechanical straight line
scanning provides the frame rate of 1 to 10 Hz and the sector scanning up to 140 Hz,
so that small animal imaging required high frame rate usually uses the mechanical
sector scanning. As the frame rate goes up, however, imaging systems suffer from
the jitter of motor position causing images moving left and right. In order to obtain
11
good quality images, therefore, the sophisticated design of a motor controller is
inevitable.
1.4 Objective of Research
(a)
(b)
Figure 1-2: Conceptual diagram of mechanical scanning divided into (a)
mechanical straight line scanning and (b) sector scanning with single element or
annular array transducers.
12
High frequency ultrasound has a great potential as a new diagnostic tool
because of its high spatial and temporal resolutions as mentioned in Section 1.2. In
order to realize this potential, however, we have to overcome the challenges which
are fabricating high performance transducers and developing dedicated hardware
systems depending on the scanning methods and the types of transducers as
mentioned in Section 1.3. From system’s point of view, especially, the dedicated
hardware systems have to be capable of reliably operating at high-speed clock rate
with very robust noise tolerance and providing a wide bandwidth for data transfer.
This is so because the frequencies of ultrasound waveforms generated by high
frequency transducers are much higher than these by conventional transducers.
Several investigators have tried to overcome the challenges and have reported
the implementation of the systems for linear array transducers (Hu et al., 2006),
annular array transducers (Brown et al., 2005), and single element transducers
(Foster et al., 1993). However, these reports have focused on only the front-end of
the systems related to data acquisition involving a transmit/receive beamformer
and/or a motor controller.
In terms of a real time modality, ultrasound imaging systems inevitably involve
a back-end processing system as well, which is responsible for extracting clinically
useful information from the acquired echo signals and displaying the information on
a monitor. To maximize advantages of high frequency ultrasound imaging, i.e., a fine
spatial and a fine temporal resolution, especially, the back-end processing system has
13
to be capable of providing very fast visualization of the extracted information
without degrading spatial resolution. In order to achieve this requirement, new signal
processing algorithms should be developed.
The goal of this research is to develop a suitable back-end processing system
for high frequency ultrasound B-mode imaging, in which a DC canceller, a time gain
compensator, an envelope detector, a logarithmic compressor, and a digital scan
converter are involved. This thesis describes the work that has been undertaken and
will be pursued in developing appropriate algorithms for high speed back-end
processing. The performances of the system developed are evaluated with the
following experiments: processing speed test of the system, wire phantom imaging,
in vitro pig eye imaging, and in vivo mouse heart imaging. As a result, it is shown
that the high processing speed of the system developed allows the cardiac imaging of
the mouse in real time where the heart rate is 5-10 beats per second.
1.5 Overview
The thesis consists of six chapters including the introduction of high frequency
ultrasound imaging in Chapter 1. Chapter 2 describes the functions of the back-end
processing in conventional ultrasound imaging system and conventional algorithms
used to realize these functions. In this chapter, the requirements of the back-end
processing system to support high frequency ultrasound imaging are defined. In
14
Chapter 3, details on a novel envelope detector with capability of logarithmic
compression that has the capability of providing very fast processing with negligible
error, i.e., within rounding error are given. Its performances are verified by
experimental results. Chapter 4 describes each functional block in the designed high
speed digital scan converter. In Chapter 5, a high-speed back-end system developed
for sector scanners is described and its performances are verified by experimental
results. Chapter 6 summaries the work and discusses possible future work.
15
CHAPTER 2
BACK-END PROCESSING
IN ULTRASOUND B-MODE IMAGING SYSTEM
2.1 General
Conventional ultrasound imaging systems can be divided into a front-end
subsystem and a back-end subsystem as shown in Figure 2-1. The front-end
subsystem plays the role of transmitting ultrasound, receiving echo signals, and
improving signal-to-noise ratio. On transmit, an array transducer is electronically
focused typically at a fixed imaging depth. In order to do so, the transmit (TX)
beamformer calculates time delay of each active element of the array transducer and
the transmitter excites the each element following the predetermined time delay.
Echo signals received at the elements are boosted by preamplifiers in the analog
receiver block. The preamplifiers are positioned as close to a transducer as possible
and its gain is determined by the sensitivity of a transducer and the input capability
of an analog-to-digital converter (ADC). The sampling rate of ADC is typically at
least four times higher than the center frequency of a transducer. Digitized echo
signals at each element are sent to the receive (RX) beamformer in order to perform
receive focusing. The RX Beamformer is one of main factors determining the
performance of ultrasound imaging systems so that many studies have been devoted
16
to the development of superior beamforming techniques (Mucci, 1984; Song et al.,
1990; O’Donnell et al., 1990). Focused echo signals frequently contain DC
component generated by the preamplifier and ADC. Since envelope detection is
carried out with echo signals without DC component, it should be suppressed below
(a)
(b)
Figure 2-1: Block diagram of generic ultrasound imaging system: (a) Front-end
subsystem and (b) Back-end subsystem for B-mode imaging (gray box), color
flow (CF) imaging, and Doppler processing.
17
a certain level. The DC canceller is responsible for removing the DC component.
The digital time-gain compensation (TGC) block cooperates with an analog TGC in
the analog receiver block to increase the amplitude of the echo signals along with
imaging depth to compensate for energy loss caused by ultrasound attenuation and
beam diffraction.
In the back-end subsystem, clinically useful information is extracted from the
echo signals. For B-mode imaging, an envelope detector, a logarithmic (LOG)
compressor, an image processor, and a digital scan converter (DSC) are involved.
Typically, clinically meaningful information about tissues is contained in the
envelope variation of echo signals arising from different tissues. An envelope
detector performs the function of removing the carrier signal and computing
envelope values from echo signals. Enveloped echo signals are logarithmically
compressed in a LOG compressor for efficient visualization. Transducers and the
analog receiver block respond to a large range of amplitude of echo signals, which is
usually over 100 dB. The functions before a LOG compressor should have the
capability to deal with this large dynamic range in order to receive very weak signals
attenuated from objects positioned at a deep depth of an imaging plane. On the other
hand, the dynamic range of display devices is around 40 dB. However, the clinically
meaningful amplitude variations of echo signals are at least 60 dB, so that it cannot
be directly displayed on a monitor without information loss (Zagzebski, 1996). A
LOG compressor is a way to overcome this problem. Small amplitude signals are
raised by reducing the large dynamic range in the LOG compressor, thus being
18
accentuated on a display device allowing the retention of clinically useful
information. After the LOG compression, an image processor carries out focal zone
blending, edge enhancement, auto gain control (AGC), black hole/noise spike filling,
lateral filtering, and persistence in order to achieve high image quality (Phelps et al.,
2004). These methods are employed in high-end ultrasound imaging systems to
generate the best possible images with superior contrast, spatial resolution, and
image uniformity (Szabo, 2004). The manipulated echo signals are mapped onto
pixels of a monitor following echo amplitude vs. gray scale conversion. However,
each sample point of the echo signals cannot be directly mapped onto each pixel
sometimes because its spatial location does not correspond to a pixel. This
mismatching problem is especially serious in the sector scanning as shown in Figure
1-1 (b) and Figure 1-2 (b) since samples are acquired in a polar coordinate system,
contrary to pixels which are arranged in a Cartesian coordinate system. Under these
circumstances, therefore, scan conversion processing is necessary to find appropriate
pixel values from the echo samples through coordinate transformation and data
interpolation.
Color flow (CF) and Doppler systems in Figure 2-1 (b) are functional
ultrasound imaging methods using the Doppler effect to evaluate the vascular system
in a noninvasive way. Two-dimensional CF images provide both the direction and
the mean velocity of blood flow by different colors and their intensity, respectively.
Although the information can be represented in different ways, commonly red and
blue colors indicate blood flow toward and away from a transducer, respectively.
19
The shade of a color is used to indicate the magnitude of blood flow speed (Shung,
2005). The CF system combined with B-mode imaging system is capable of
providing anatomical and blood flow information on clinical problems such as jets
from the stenotic vessels and leaking heart valves, flow reduction, and occlusion
from atherosclerotic plaque (Szabo, 2004). Contrary to the 2-D CF imaging, the
Doppler system obtained instantaneous blood flow velocity at a certain point called
the range gate in pulsed wave (PW) mode or at a intersection point of transmit and
receive beams in continuous wave (CW) mode. Doppler data can be transformed into
frequency domain in the spectrum analyzer in Figure 2-1 (b). The Doppler spectrum
data show the variation of flow velocity along time. Through an audio processor, in
addition, the Doppler data may become audible. With the Doppler spectrum and the
audible Doppler data, it is possible to diagnose cardiac activity of a fetus and a
stenotic valve and to estimate volume flow and a quantitative measure of the breadth
of the velocity (Szabo, 2004). More recently, the CF and Doppler system with
contrast agents have been shown to be a potential method of molecular imaging
(Liang and Blomley, 2003).
2.2 Envelope Detector
The amplitude variations of zero-offset echo signals are obtained in an
envelope detector. The envelope detection can be carried out by different algorithms
20
classified into four types of varying levels of accuracy and complexity. In this
section, each type of algorithm is briefly reviewed and its accuracy is examined by
computer simulation with a real echo data shown in Figure 2-2 by using MATLAB
Figure 2-2: Echo signal used in simulation to examine the level of accuracy of
envelope detection algorithms. The plot shows normalized 8-bit echo data from a
20 MHz annular transducer sampled at 500 MHz through an oscilloscope (a) and
its frequency spectrum (b).
21
(MathWorks Inc., Natick, MA). In the simulation, 8-bit echo data from a 20-MHz
single element transducer sampled at 500 MHz through an oscilloscope (Lecroy
LC534, Chestnut Ridge, NY) were used. The -6 dB bandwidth of the transducer was
60 % and the echo data contained a second harmonic component of -40 dB level and
the cutoff frequency of 33-tap low pass filters (LPF) used in the simulation was 12
MHz. The accuracy of each algorithm was quantified by using root mean square
error (RMSE) between envelope data obtained by practical algorithms and the ideal
Hilbert transformer. The RMSE values were normalized with respect to the root
mean square (RMS) value of the ideal envelope data extracted by the ideal Hilbert
transformer. The RMS and normalized RMSE values were calculated by using the
following equations:
()
2
11
1
[, ]
MN
ideal
mn
RMS X m n
MN
==
=
⋅
∑∑
(2−1)
()
2
11
1
[, ] [ , ]
100
MN
ideal
mn
norm
Xmn Xmn
MN
RMSE
RMS
==
−
⋅
=×
∑∑
(2−2)
where
ideal
X is the ideal envelope data set represented by M N × matrix and X is a
target envelope data set to evaluate its accuracy.
2.2.1 Ideal Hilbert Transformer
It is well known that a received echo signal ( ) rn sampled at an interval
S
T can
22
be expressed as
( ) ( ) ( )
0
cos
SSn
rn A nT n T ω φ =⋅ + (2−3)
where ()
s
A nT is the envelope information,
0
ω is the center frequency of the echo
signal, and
n
φ is phase angle varying with time. This received echo signal can be
decomposed into its in-phase and quadrature components as
() ( ) ( ) ( ) ( ) ( )()
() ( ) () ( )
00
00
cos cos sin sin
cos sin
s sn s s n
Is s Q s s
rn A nT n T A nT n T
AnT n T A nT n T
ω φωφ
ωω
=⋅ ⋅ − ⋅ ⋅
=⋅ − ⋅
(2−4)
where ( )
I s
A nT and ()
Qs
A nT represent the in-phase and the quadrature components
of the received echo signal, respectively. By Hilbert transform, the analytic signal
can be obtained.
( ) ( ) ( )
aHT
rn r n jr n =+⋅ (2−5)
where
() ( ) ( ) ( ) ( )
00
cos sin
HTQs s I s s
rn A nT n T A nT n T ωω =+ (2−6)
The envelope information can be obtained by computing the magnitude of
Equation (2-5) through the square root of the sum of the squares of () rn and ()
HT
rn .
In this work, the envelope data obtained from this ideal Hilbert transformer is used as
a gold standard for comparison of the accuracy of each algorithm.
2.2.2 Rectification of RF Signal Followed by Filter
23
Rectifying the received echo signals is the simplest method for envelope
detection. If phase angle
n
φ is zero, Equation (2-3) can be replaced by a Fourier
series after taking absolute value.
() ( ) ( )
()
()
()
0
1
0 2
1
cos
1
24
cos 2
41
ss
k
ss
k
rn A nT n T
A nT kn T
k
ω
ω
ππ
+
∞
=
=⋅
⎡ ⎤
−
=⋅+ ⋅ ⎢ ⎥
−
⎢ ⎥
⎣ ⎦
∑
(2−7)
where it is assumed that the envelope information ()
s
A nT is a positive value. After
low pass filtering with a cutoff frequency in a frequency interval determined by
0
ω
and a half bandwidth of the envelope signal, the envelope information is obtained as
follows:
() () ()
2
s
LPF
K
En rn A nT
π
⎡⎤
==⋅
⎣⎦
(2−8)
where K is the gain of LPF.
Although a median filter can be used in a software-based implementation
instead of LPF (Schlaikjer et al., 2003), the accuracy of the LPF method is superior
to that of the median filter method. This is clearly seen in Figure 2-3, where the
envelope information of the received echo signal (gray dotted line) extracted by the
rectifiers with a median filter (gray dashed dot line) and LPF (dashed line) is
presented. In order to quantify their accuracy, RMSE between the obtained envelope
information and the ideal envelope information extracted by the ideal Hilbert
transformer (solid line in Figure 2-3) was calculated. The normalized RMSE values
of the rectifier with a median filter and LPF are 13.35 % and 7 %, respectively.
24
In spite of its simplicity, this algorithm cannot be used for high frequency
ultrasound systems which employ the quadrature sampling technology to reduce
sampling speed (Song et al., 1990; Brown et al., 2005). Another drawback of this
algorithm is that the second harmonic component of ( )
s
A nT distorts the baseband
signal obtained by taking the absolute value of the original echo signal. Furthermore,
this algorithm always introduces aliasing caused by sampling because Equation (2-7)
Figure 2-3: Accuracy of the envelope information extracted by the rectifier with a
median filter (gray dashed dot line) and the rectifier with LPF (dashed line). As a
gold standard of the accuracy, the envelope information extracted by the ideal
Hilbert transformer (solid line) is presented.
25
is not a band-limited signal although the magnitude of harmonic components
generated by ()
0
cos 2
s
kn T ω is drastically decreased with its order. In addition, this
algorithm is hardly used in a commercial ultrasound system because it cannot
provide phase information needed for Doppler and color flow imaging.
2.2.3 Approximate Hilbert Transformer
Because the transfer function of the Hilbert transformer has discontinuities at
zero frequency and at half of the sampling frequency, the direct utilization of the
transfer function is impossible in time domain. As an approximate version, therefore,
a well designed FIR or IIR Hilbert filter can be used to generate Hilbert transformed
data of the received echo signal (Oppenheim et al., 1998; Koll ár et al., 1990; Tomov
and Jensen, 2005). The block diagram of the envelope detector using the Hilbert
filter is shown in Figure 2-4 (a). From the simulation results shown in Figure 2-5, it
is seen that the envelope information from this method (dashed line) comes close to
the ideal envelope (solid line). The normalized RMSE value of this method was
6.21 % although it can be decreased by using a large number of filter taps (more than
one hundred). A drawback of this method is that it is difficult to remove the
imbalance of two different signal paths, i.e., different frequency responses of a band
pass filter (or all pass filter) and a Hilbert filter. This imbalance can be a more crucial
problem in Doppler and color flow imaging rather than B-mode imaging.
26
Another approximate Hilbert transformer is obtained by delaying the original
echo data by α samples corresponding to shifting a 90 degree phase from the center
frequency of the received echo data as shown in Figure 2-4 (b) (Koll ár et al., 1990).
This method can provide acceptable accuracy when the received signal has a high
quality factor Q, otherwise causing a serious error in the detected envelope (Song
(a)
(b)
Figure 2-4: Block diagram of envelop detectors realized by the Hilbert filter
method (a) and the time delay method (b) including logarithmic compression
function. () rn is digitized echo signal, ( )
env
rn is logarithmic-compressed
envelope information, α represents the number of delay samples corresponding
to shifting a 90 degree phase from the center frequency
0
ω of the received echo
data, and
s
T is sampling period.
27
and Park, 1990). Because the ultrasound pulse usually has a relative low Q, a very
fast sampling clock is required to use the time delay method. This requirement is not
easy to satisfy in high frequency ultrasound imaging systems.
In Figure 2-5, it is easily seen that the Hilbert filter method (dashed line) has a
superior accuracy to the time delay method (gray dashed dot line) under the
condition where those envelope shapes fluctuate in the vicinity of the ideal envelope
information (solid line). The normalized RMSE of the time delay method was
Figure 2-5: Accuracy of the envelope information extracted by the time delay
method (gray dashed dot line) and the Hilbert filter method (dashed line)
compared with the outcome from the ideal Hilbert transformer (solid line).
28
17.60 %, which is about three times higher than that of the Hilbert filter method, i.e.,
6.21 %. In addition to the poor accuracy, the time delay method cannot be used for
Doppler and color flow imaging due to severe phase distortion. In this method, in
fact, it is assumed that ( ) ( )
Is Is
AnT A nT α ≈ − and ( )( )
Qs Qs
AnT A nT α ≈− .
Although the assumption is completely satisfied, time delay of α is the key factor
resulting in the phase distortion of the Hilbert transformed signal.
2.2.4 Quadrature Demodulation
Quadrature demodulation is commonly used in Doppler and color flow
Figure 2-6: Block diagram of the envelope detector realized by the quadrature
demodulation method.
29
imaging system (Nitzpon et al., 1995; Szabo, 2004). This method generates the
baseband in-phase and quadrature components by mixing with sine and cosine
waveforms and carrying out low pass filtering as shown in Figure 2-6. The generated
complex baseband components can be expressed as follows:
( ) ( ) ( )
() ( )
0
cos
cos
2
s
LPF
sn
In r n n T
K
AnT
ω
φ
⎡ ⎤ =⋅
⎣ ⎦
=⋅ ⋅
(2−9)
Figure 2-7: Accuracy of the envelope information extracted by quadrature
demodulation (dashed line) compared with the outcome from the Hilbert filtering
(gray dashed dot line) and the ideal Hilbert transforming (solid line).
30
( ) ( ) ( )
() ( )
0
sin
sin
2
s
LPF
sn
Qn r n n T
K
AnT
ω
φ
⎡ ⎤ =⋅
⎣ ⎦
=− ⋅ ⋅
(2−10)
where K is the gain of LPF. With the complex baseband signals, finally, the envelope
information is obtained by the following calculation.
() () () ()
22
2
s
K
En I n Q n A nT =+ =⋅ (2−11)
In Figure 2-7, the results from the quadrature demodulation method (dashed
line) and Hilbert filter method (gray dashed dot line) are presented to illustrate the
accuracy of the two methods. The normalized RMSE of the quadrature demodulation
method was 5.18 %, which was the smallest value in the simulation.
Table 2-1 shows the summary of the normalized RMSE values of the envelope
Table 2-1: Summary of the normalized RMSE values of the envelope detection
algorithms
Rectifier method
Approximate Hilbert
transform method
Median
filter
LPF
Time
Delay
Hilbert
filter
Quadrature
demodulation
method
norm
RMSE
13.35 % 7.00 % 17.60 % 6.21 % 5.18 %
31
detection algorithms. From this table, it is seen that the quadrature demodulation
method is capable of providing the best accuracy and the Hilbert filter method
occupies the second place. As a result, the Hilbert filter and the quadrature
demodulation methods can be a candidate for the envelope detection algorithm used
in a high frame rate high frequency ultrasound imaging system if we can implement
the methods so that they can operate at a very high speed.
2.3 Logarithmic Compressor
Generally, logarithmic compression can be interpreted as an amplitude
mapping process in the logarithmic domain for better visualization. If an k-bit gray
scale logarithmic compressor is applied to the envelope data () En , the compressed
envelope data can be written as:
()
( )
log 10
min
20 2
log
k
En
En B
DR E
⎛⎞
×
= ⋅+
⎜⎟
⎝⎠
(2−12)
where B is a gain factor and DR stands for dynamic range defined as the difference
between the strongest and the weakest data (
max
E and
min
E ) in logarithmic scale and
can be expressed as ( ) ( )
10 max 10 min
20 log 20 log EE ⋅−⋅ . The entire system dynamic
range including a transducer determines the dynamic range of a logarithmic
compressor. The weakest envelope datum
min
E means a noise threshold below which
the noise is removed. Input data values larger than the strongest envelope datum
32
max
E are mapped to the saturation value of the output which is 255 in case of output
data represented by 8 bits. Figure 2-8 shows a logarithmic compression characteristic
plot for different DRs. In this plot, 12-bit input binary data and 8-bit output binary
data are assumed.
Since logarithmic compressor carries out a nonlinear transform on the envelope
Figure 2-8: logarithmic compression characteristic plot along different dynamic
range (DR). In this plot, input binary data are represented by 12 bits and output
binary data are represented by 8 bits. Input data values larger than
max
E are
mapped to the saturation value of the output, 255 in this case.
33
data, it is more efficient to implement it with a look-up table (LUT) method than to
compute it by an algorithm in terms of accuracy and operating speed. A RAM-type
memory can be used as LUT in direct implementation of logarithmic compressor. In
order to contain values shown in Figure 2-8, for example, the LUT should have 12-
bit indices and 8-bit entries, which can be realized with a 4-Kbytes memory. In
practice, however, a ROM-type memory for logarithmic transform and several
RAM-type memories for parameters are used at the expense of a slight increase of
hardware complexity in order to reduce the time needed to update LUT entries
whenever either a noise threshold or DR is changed. This is because it is only
required to update small size RAM-type memories with new values. Figure 2-9 is an
implementation example of a logarithmic compressor for the fast update of
parameters.
Figure 2-9: An implementation example of logarithmic compressors for fast
update of parameters. The scale factors in the second RAM block stand for the
values of 20 2
k
DR × as shown in Equation (2-12). In this implementation, the
gain factor B is set to zero.
34
2.4 Digital Scan Converter (DSC)
Scan conversion is a procedure to map acquired echo samples onto pixels of a
monitor. The simplest method is to assign a value of the nearest echo sample to the
pixel (Ophir and Maklad, 1979). However, the echo samples are typically more
abundant in the axial direction but fewer in the lateral direction. When the samples
are mapped onto pixels, pixels located in between two scanlines may not be assigned
with any samples, causing the Moiré artifact. This phenomenon is obvious in sector
scanning method shown in Figure 1-1 (b) and 1-2 (b) because pixels located far from
a transducer have a less possibility to be assigned with a sample. Therefore, the scan
conversion mainly involves data interpolation requiring coordinate transformation of
pixels from a Cartesian coordinate to a polar coordinate in case of sector scanning.
Various data interpolation algorithms were proposed and their performances were
examined (Larsen and Leavitt, 1980; Robinson and Knight, 1982; Lee et al., 1986;
Berkhoff et al., 1994; Richard and Arthur, 1994; Hwang and Song, 2001). Bilinear
interpolation is known as the best algorithm among these algorithms in terms of
accuracy and processing speed although it requires relatively high complexity for
realization (Lee et al., 1986).
Bilinear interpolation is two-dimensional interpolation: the first order Lagrange
interpolation (Laasko et al., 1996), called linear interpolation, along radial and
angular directions. Therefore, the value of a pixel P in Figure 2-10 can be obtained
by the following calculations.
35
12 3 1
12
22 4 1
1
12
i
i
SR S R
I
RR
SR SR
I
RR
+
× +×
=
+
× +×
=
+
(2−13)
1 ii
P
II
A
α β
αβ
+
× +×
=
+
(2−14)
where
1
S to
4
S are the values of samples surrounding the object pixel P , α and β
are angular differences between P and two scanlines
i
SL and
1 i
SL
+
, and
1
R and
2
R
are radial differences between P and two samples located on either
i
SL or
1 i
SL
+
.
i
I
and
1 i
I
+
are intermediate values on two scanlines
i
SL and
1 i
SL
+
, respectively.
Linear interpolation is a simplified version of bilinear interpolation. Unlike
bilinear interpolation, linear interpolation involves only angular interpolation given
by
12
P
SS
A
α β
αβ
× +×
=
+
(2−15)
where
1
S and
2
S are selected because they are the nearest samples to P along radius
direction. Although linear interpolation is easily implemented and saves operating
time to fetch stored samples for data interpolation, its accuracy is inferior to bilinear
interpolation if the number of samples in the radial direction is small. If the sampling
rate along radial direction is increased, the accuracy of linear interpolation would be
improved. Richard and Arthur (1994) verified it with various B-mode images that if
being performed with envelope data over-sampled by a factor of 2 or more, linear
interpolation can provide superior image quality to bilinear interpolation with the
36
original data that are sampled to match pixel-to-pixel spacing. This result sheds light
on the relationship between the number of samples along radial direction and the
improvement of the accuracy of linear interpolation. It is, however, not sufficient
with respect to the comparison of accuracy between the two algorithms because the
accuracy of bilinear interpolation can be improved with the over-sampled envelope
data as well. Intuitively, bilinear interpolation would have superior or equal accuracy
to linear interpolation if the same number of envelope samples is involved in each
processing. In order to decide whether a sampling rate making linear interpolation
Figure 2-10: Conceptual representation of bilinear and linear interpolation
37
provides an acceptable image quality, it is necessary to quantitatively compare the
accuracy of linear and bilinear interpolation in the situation where the same number
of envelope samples is used for the processing.
2.4.1 Accuracy of Linear Interpolation
The comparison of accuracy of the two algorithms was undertaken by using the
Field II simulation program (Jensen and Svendsen, 1992; Jensen, 1996). In the
simulation, a 40-MHz single element transducer model was used. Its focal point was
8 mm, F-number was 2.5, and spectrum had the bandwidth of 40 MHz. Five targets,
1.4 mm apart along lateral direction at the focal depth of 8 mm, were scanned by
means of the mechanical sector scanning in which the viewing angle was 50 degrees
and 181 number of scanlines were used. Echo signals were acquired at the sampling
rate of 800 MHz and Hilbert transformation was carried out to extract the exact
envelope information from the echo signals. After the ideal envelope detection, the
information was logarithmically compressed with a 72 dB dynamic range so that it
can be used for each interpolation algorithm.
Once the locations of pixels are transformed from a Cartesian coordinate to a
polar coordinate, each pixel has a unique angle and radius. Wanting to obtain a pixel
value without the error caused by both radial and angular interpolation, we can rotate
a transducer by the angle of a pixel and select an envelope sample corresponding to
38
the radius of the pixel among the samples generated at extremely high sampling rate
like 2 GHz. By repeating the procedure for the entire pixels, we can obtain an error-
free image. In the simulation, a standard image used for the comparison was formed
with this method.
In common ultrasound imaging systems, baseband echo samples obtained by
quadrature demodulation are decimated along with the bandwidth of the samples.
This is possible because the sampling rate of the systems for radio-frequency echo
signals is much higher than the bandwidth of their baseband counterpart. The factor
of decimation can be increased until the new sampling rate satisfies the Nyquist rate
for the baseband signals. By doing so, the square root function shown in Equation (2-
11) can be given enough time to compute envelope data as well as a small amount of
memory can be used to store the results. From the point of view of displaying images
on a monitor, the space between two adjacent pixels is also determined so that it can
satisfy at least the Nyquist rate for the envelope signals to avoid Moiré artifact once
an image depth for displaying is chosen. Therefore, the simulation was performed
with the two pixel-to-pixel spaces of 37 m μ and 18.5 m μ corresponding to one and
two times Nyquist rate for baseband signals, respectively. DSC with linear and
bilinear interpolation was performed with the various factors of decimation, i.e., the
various sampling rates under the each pixel-to-pixel space. The accuracy of each
interpolation algorithm along with a sampling rate was evaluated by compute the
normalized RMSE between pixel values obtained by the each algorithm and exact
pixel values. Table 2-2 shows the normalized RMSE values along with each pixel-to-
39
pixel space.
As expected above, it is seen from Table 2-2 that bilinear interpolation is
Table 2-2: Comparison of accuracy of the linear interpolation and the bilinear
interpolation algorithms by computer simulation using Field II program; the
accuracy of each algorithm was evaluated with the normalized RMSE between
pixel values obtained by each interpolation algorithm and exact pixel values. In
this table,
s
f is a sampling frequency and
max
f is the highest frequency of
baseband echo signals of 20 MHz in the simulation.
(a) A pixel-to-pixel space of
max
2 f
s
f
algorithm
max
2 f
max
4 f
max
5 f
max
8 f
max
10 f
max
20 f
Bilinear
Interpolation
8.56 % 7.40 % 7.30 % 7.21 % 7.13 % 7.12 %
Linear
Interpolation
12.19 % 9.46 % 9.00 % 7.86 % 7.72 % 7.40 %
Differences 3.63 % 2.06 % 1.70 % 0.65 % 0.59 % 0.28 %
(b) A pixel-to-pixel space of
max
4 f
s
f
algorithm
max
2 f
max
4 f
max
5 f
max
8 f
max
10 f
max
20 f
Bilinear
Interpolation
8.77 % 7.08 % 6.68 % 6.38 % 6.36 % 6.28 %
Linear
Interpolation
12.79 % 9.21 % 8.89 % 7.12 % 6.63 % 6.55 %
Differences 4.02 % 2.13 % 2.21 % 0.74 % 0.27 % 0.27 %
40
always capable of providing the superior accuracy to linear interpolation even though
sampling rate increases. However, the differences between the accuracy of the two
algorithms tend to decrease with sampling rate; these become below 1 % from the
sampling rate of
max
8 f that is four times higher than the Nyquist rate for the baseband
component of the echo signals obtained by Equation (2-11). With the sampling rate,
linear interpolation is capable of providing comparable image quality to bilinear
interpolation.
Figure 2-11 shows point target images obtained by the Field II simulation when
a sampling rate is 40 MHz (
max
2 f ) and the pixel-to-pixel space is 18.5 m μ . The
images in top, middle, and bottom panels were obtained by the exact solution, DSC
with bilinear interpolation, and DSC with linear interpolation, respectively. From this
figure, we can learn that the error from linear interpolation makes the image of the
point targets, located in -2.8 mm and -1.4 mm, blocky although bilinear counterpart
makes it a little blur. However, a point target image located in the center scanline,
i.e., 0 mm in the lateral direction shows almost same quality in both cases. As a result,
it can be said that interpolation error mainly affects an image of targets apart from
the center scanline rather than these in vicinity of the center scanline. This is easily
seen from Figure 2-12 illustrating lateral beam profiles of the three point targets
located in 0 mm (top panel), -1.4 mm (middle panel), and -2.8 mm (bottom panel).
The error imposed on the lateral beam profile in the top panel appears to be below -
60 dB level in cases of both linear and bilinear interpolation. But it in the middle and
bottom panels is shown around the entire profile in both cases. In case of linear
41
interpolation, especially, the off-center lateral beam profiles look like stairs due to
the lack of envelope samples, which make images blocky. However, this problem is
alleviated as sampling rate augments. It can be seen from Figure 2-13 and Figure 2-
14 illustrating point target images obtained with a sampling rate of 100 MHz (
max
5 f )
and their lateral beam profiles, respectively.
The sampling rate of 100 MHz is still a little bit slow for linear interpolation to
Figure 2-11: Point target images obtained when a sampling rate is 40 MHz
(
max
2 f ) and the pixel-to-pixel space is 18.5 m μ . The images in top, middle, and
bottom panels were obtained by the exact solution, DSC with bilinear
interpolation, and DSC with linear interpolation, respectively.
42
provide acceptable image quality meaning that the difference of the RMES values of
linear and bilinear interpolation becomes below 1 %. With this sampling rate,
Figure 2-12: Lateral beam profiles of three point targets shown in Figure 2-11.
Top panel is for a point target at 0 mm in lateral direction and 8 mm in axial
direction, middle panel is for it at -1.4 mm and 8 mm, and bottom panel is for it at
-2.8 mm and 8 mm.
43
however, the image obtained with linear interpolation (bottom panel in Figure 2-13)
appears to be much smoother than the previous one. In addition, its lateral beam
profiles shown in Figure 2-14 become similar to these obtained with bilinear
interpolation.
Figure 2-13: Point target images obtained when a sampling rate is 100 MHz
(
max
5 f ) and the pixel-to-pixel space is 18.5 m μ . The images in top, middle, and
bottom panels were obtained by the exact solution, DSC with bilinear
interpolation, and DSC with linear interpolation, respectively.
44
If one wants to use linear interpolation to implement DSC operating at a very
high speed with the acceptable image quality, as a result, the sampling rate of
Figure 2-14: Lateral beam profiles of three point targets shown in Figure 2-13.
Top panel is for a point target at 0 mm in lateral direction and 8 mm in axial
direction, middle panel is for it at -1.4 mm and 8 mm, and bottom panel is for it at
-2.8 mm and 8 mm.
45
envelope samples should be four times higher than the Nyquist rate for the baseband
component of echo signals. This requirement can be achieved by either radial
interpolation with decimated envelope samples (Richard and Arthur, 1994) or a very
high-speed envelope detector capable of generating envelope samples at the same
rate of the sampling clock of systems (Chang et al., 2007).
2.5 System Requirements for High Frequency Ultrasound Imaging
In general, 20 MHz to 50 MHz transducers are mainly used for high frequency
ultrasound imaging that requires not only a fine spatial resolution, but also a fine
temporal resolution. Therefore, the sampling frequency of the imaging systems
should be more than 200 MHz to meet the Nyquist rate for echo signals. The -6dB
bandwidth of the transducers usually has the range between 50 and 100 percentage of
their center frequency. For 50 MHz transducers, the maximum -6dB bandwidth will
be 50 MHz, so that the image pixel spacing of a back-end processing system should
be less than 30.8 m μ (
6
1540 2 25 10 ×× ). Because of a small region of interest in
high frequency ultrasound imaging, the minimum height of an image can be
determined by the size of the mouse heart, i.e., around 5 mm in short axis. With the
maximum image pixel spacing and the minimum height of an image, we can
determine the minimum number of pixels in axial direction that is 163. If the number
of pixels is 256, an image will cover 62.41
2
mm imaging area (7.9 × 7.9 mm).
46
The space between two adjacent scanlines is determined by the lateral
resolution of transducers, which is expressed as Equation (1-1). Since general high
frequency transducers have the minimum F-number of 2.0, the lateral resolution of
50 MHz transducer is about 61.6 m μ (30.8 m μ × 2) in a focal depth. Therefore, the
space between two adjacent scanlines should be less than a half of this value, i.e.,
30.8 m μ . Under the assumption of the maximum view angle of 40 degrees and the
maximum imaging depth of 20 mm, it is sufficient that the back-end processing
system can deal with 256 scanlines in order to satisfy the required scanline space. If
the frame rate of imaging systems is 100 images per second that is the minimum
requirement to acquire mouse heart activities, DSC should be completed with 10 ms
(1/100). In addition, envelope detection and logarithmic compression for a scanline
should be completed with 39.1 s μ (10 256 ms ). This is so because the envelope
detection and logarithmic compression are usually carried out in parallel with other
back-end processing such as DSC. Data transfer rate between a DSC and a display
module should be at least 27 Mbytes per second. This value can be calculated by
multiplying the frame rate by the number of pixels constituting an image. If the
frame rate is 100 images per second and an image consists of 256,144 pixels (512 by
512 image size), the data transfer rate will be 27 Mbytes per second that corresponds
to the frame rate of 400 images per second with 256 by 256 image size. Table 2-3
shows the summary of system requirements for high frequency ultrasound B-mode
imaging.
47
Table 2-3: Summary of system requirements for high frequency ultrasound
B-mode imaging
Minimum sampling clock rate 200 MHz
Maximum image pixel spacing (S)
30.8 m μ
Minimum image height (H) 5 mm
Minimum number of pixels (H/S) in axial direction 163
Maximum number of scanlines 256
Minimum frame Rate 100 images/s
Maximum processing time for envelope detection
and logarithmic compression per scanline
39.1 s μ
Maximum processing time for DSC per image 10 ms
Minimum data transfer rate to a display module 27 Mbytes/s
48
CHAPTER 3
A NOVEL ENVELOPE DETECTOR FOR HIGH FRAME RATE,
HIGH FREQUENCY ULTRASOUND IMAGING
3.1 Introduction
Conventional medical ultrasound imaging system involves an envelope
detector and a logarithmic compressor to extract the magnitude of echo signals and
to logarithmically compress the magnitude information for better visualization,
respectively. While logarithmic compression is usually implemented with the look-
up table (LUT) method, the extraction of signal magnitude can be realized with
various algorithms in hardware or software as reviewed in the previous chapter. A
typical algorithm involves extracting analytical signals from received echo signals by
using Hilbert transform and computing its magnitude by the square root of the sum
of the squares of the real and the imaginary parts in the analytic signals. Although
being capable of yielding the exact envelope and phase information from the analytic
signals, this type of method is seldom used in commercial ultrasound imaging
systems because of the involvement of a direct and an inverse Fourier transform
requiring considerable overhead in processing time, which is both costly and more
complex to implement. To realize the extracting of the analytic signals from the
received echo data in real time, two different approximate Hilbert transform methods
49
have been used: FIR or IIR Hilbert filter method (Koll ár et al., 1990; Oppenheim et
al., 1998; Tomov and Jensen, 2005) and time delay method (Song and Park, 1990;
Schlaikjer et al., 2003). The most commonly used algorithm in commercial
ultrasound imaging systems, however, is the quadrature demodulation technique
generating the baseband in-phase and quadrature components of received echo
signals instead of the analytic signals (Song and Park, 1990; Sikdar et al., 2003; Kim
et al., 2004).
The magnitude of either the analytic or the complex baseband signal is
calculated with a square root function, which can be realized by several algorithms
(Volder, 1959; Prado and Alcantara, 1987; Montuschi and Mezzalama, 1990). In a
small animal cardiac imaging system requiring a very high frame rate, the square
root function implemented by these algorithms must be capable of operation at very
high speed. This is because the frame rate for the small animal cardiac imaging
should be more than 100 frames per second (Foster et al., 2000; Xu et al., 2005); thus
the back-end processing including a digital scan converter should be performed in
less than 10 ms for a frame. Because the envelope detection including logarithmic
compression is usually carried out in parallel with other back-end processing, the
envelope detector can spend the entire time of 10 ms for its task. This means that the
envelope detection for a scanline should be completed within 39.1 s μ in the case of
256 scanlines. Hardware implementation of square root algorithms would satisfy the
requirement for the small animal cardiac imaging at the cost of a sophisticated design,
especially for high sampling frequency systems such as high frequency ultrasound
50
imaging systems as mentioned in the Chapter 1. On the other hand, software-based
counterparts using a commercial digital signal processor (Prado and Alcantara, 1987;
Kim et al., 2004) or a media processor (Sikdar et al., 2003) demand very high-
performance processors capable of high computational throughput, large internal
memory, and high bandwidth of data transfer between internal and external
memories. These requirements are predicated upon that accurate square root values
can only be obtained by many iterative computations and data transfer operations
that frequently occur to fetch LUT values and to store the results from/to external
memories. For example, Sikdar et al. (2003) addressed that the number of operating
cycles for the square rooting and logarithmic compression of a frame consisting of
168,960 samples was 4.86 Mcycles. This number of operating cycles corresponds to
16.2 ms at a 300 MHz operating clock frequency. This processing time is too long to
allow the employment of software-based implementation of the square root
algorithms for very high frame rate small animal cardiac imaging systems.
The LUT method is capable of providing the simplest implementation of the
square root function and the fastest operation speed in both the hardware and
software if a fast and large-sized memory is available. Because the size of LUT
exponentially increases with the number of input bits, the direct use of the LUT
method to implement the square root function is hardly feasible even in a moderately
accurate system. In case of 16-bit representation each for real and imaginary
components and 8-bit representation for the output of the square root function, for
example, LUT has 32-bit wide indices and 8-bit wide entries, so that it requires at
51
least 4 Gbytes of memory (
32
288 × ÷ ), which is currently impractical for a typical
ultrasound imaging system.
This Chapter proposes a new design of the envelope detector including
Logarithmic compression which adopts the quadrature demodulation and the square
root function based on a new LUT strategy for high-frame rate high-frequency
ultrasound imaging systems. The main feature of the proposed design is that the new
LUT strategy employs a binary logarithmic number system (BLNS) (Koren, 2002)
instead of a fixed-point number system. By using BLNS, the size of LUT can be
dramatically reduced by the manipulation of square rooting equation, thus taking full
advantage of the attractive properties of the LUT method allowing fast operation
speed and accuracy as well as simple implementation. Another merit of the new LUT
strategy is that an individual logarithmic compression functional block is not
required. This is so because the result from the square root function, represented by
BLNS, is a logarithmic-compressed version of envelope information.
In this Chapter, the proposed envelope detector with BLNS is described and its
hardware-based implementation is presented although the design is also suitable for
software-based implementation. The operating time of the proposed design is
estimated and its accuracy is compared to that of an ideal envelope detector. Through
these results, it is shown that the proposed design has a superior capability for high
frame rate high frequency ultrasound imaging systems than the conventional
envelope detectors.
52
3.2 Description of Proposed Design
An envelope detector for the small animal cardiac imaging should satisfy the
following requirements:
• The entire processing should be completed within at least 10 ms for a frame
in order to support more than 100 frames per second
• An implemented system based on an envelope detection algorithm should
provide an accuracy within acceptable rounding error (i.e., less than 0.5)
compared with these from arithmetic computation of the algorithm.
• Phase information should be provided to a Doppler and color flow imaging
block.
In order to satisfy these requirements, the proposed design adopts the quadrature
demodulation method to extract the complex baseband signals including the phase
information, which is commonly used in the Doppler and color flow imaging system
(Nitzpon et al., 1995; Szabo, 2004). And the magnitude of the extracted complex
baseband signals is computed by the square root function based on a new LUT
strategy which can dramatically reduce the size of LUT through the manipulation of
square rooting equation by using BLNS.
The LUT method for implementation of square root function via Equation (2-
11) is capable of providing not only accuracy, but also fast processing speed.
However, the direct use of this method requires a tremendous amount of memory,
thus manipulating Equation (2-11) to reduce memory size is desirable. For this, the
53
envelope signal can be rewritten by
() ()
()
()
()
() () () ()
()
22
2
2
log log
1
12
In Q n
In
En Q n
Qn
Qn
−
⎛⎞
=⋅+
⎜⎟
⎜⎟
⎝⎠
⎛⎞
=⋅ +
⎜⎟
⎝⎠
(3−1)
By applying the base 2 logarithm to Equation (3-1), the logarithmic envelope signal
is then obtained as follows:
() ()
()
() () () ()
()
22
2
log log
22 2
log log log 1 2
In Q n
En Q n
−
⎛⎞
⎡⎤=+ +
⎜⎟
⎣⎦
⎝⎠
(3−2)
where ()
2
log • represents BLNS, which is an alternative way to represent binary
numbers capable of simplifying the computation of multiplication and division to
addition and subtraction, respectively (Lo and Aoki, 1985; Koren, 2002). A number
of studies have shown the efficiency of BLNS in real-time digital signal processing
applications in terms of processing time as well as accuracy (Kurokawa et al., 1980;
Vainio and Neuvo, 1986; Taylor et al., 1988). In Equation (3-2), therefore, the result
from a subtraction operation between ( ) ( )
2
log In and () ()
2
log Qn instead of a
division operation is used as an input to a LUT containing the square rooting values
and generating its outcomes in BLNS.
In a digital circuit, any positive decimal integer number N can be represented
by a m-bit fixed-point number as follows
1
0
2
m
i
i
i
Nb
−
=
= ⋅
∑
(3−3)
54
where {} 1 , 0
i
b ∈ . If the most significant bit is brought out from the summation
operator, Equation (3-3) can be rewritten as
1
0
1
0
22
21 2
l
li
li
i
l
lil
i
i
Nb b
b
−
=
−
−
=
=⋅ + ⋅
⎛⎞
=+ ⋅
⎜⎟
⎝⎠
∑
∑
(3−4)
where l is the most significant bit position at which 1
l
b = . Once the base 2
logarithm is applied to number N in order to convert it to a binary logarithmic
number, Equation (3-4) can be expressed as
()
1
22
0
log log 1 2
l
il
i
k
Nl b
−
−
=
⎛⎞
=+ + ⋅
⎜⎟
⎝⎠
∑
(3−5)
Therefore, the integer and fractional values of ( )
2
log N are l and the second term of
Equation (3-5), respectively. If number 14 is transformed to an 8-bit binary
logarithmic number with rounding, for example, it will be
210 2 2 2 10
log (14 ) log (00001110 ) 11.110100 3.8125 = = = (3−6)
The real value of ()
2
log 14 is 3.8074, so that error between the true and the 8-bit
binary logarithmic values of the number 14 is less than
6
2
−
, which is a 0.13 percent
difference.
Since the proposed design employs both the fixed-point number system for the
quadrature demodulation and BLNS for the square root function, the conversion
between two different number systems as illustrated by Equation (3-5) is required. It
can be performed by means of either a LUT method (Lo and Aoki, 1985; Wan and
55
Wey, 1999) or a computational method (Abed and Siferd, 2003). In the digital
system requiring a very fast processing time, the LUT method for both logarithmic
and antilogarithmic conversion is used. Since the accuracy of antilogarithmic
numbers is determined by the number of bits representing a binary logarithmic
number, the conversion method based on LUT needs a large size memory to obtain
precise antilogarithmic numbers. However, the proposed design does not involve the
antilogarithmic conversion because the outcome of Equation (3-2) represented by
BLNS is directly used for logarithmic compression. For the reason, a logarithmic
number in this design can be also represented by a relatively small number of bits so
that LUT can be served as the conversion method with a feasible memory size.
Logarithmic compressors play a role in reducing the large dynamic range of
received echo signals for better visualization as shown in Chapter 2. If an 8-bit gray
scale Logarithmic compressor is applied to the envelope information ( ) En ,
Equation (2-12) can be rewritten as
()
()
( )
2
2min
20 255
log
log 10
env
En
rn B
DR E
⎡⎤ ⎛⎞
×
= ⋅+
⎢⎥ ⎜⎟
⋅
⎢⎥
⎝⎠ ⎣⎦
(3−7)
where ()
env
rn is the compressed envelope data. By substituting Equation (3-2) into
Equation (3-7), the compressed envelope data is given by
() () ()
() ( )
()
()
22
2
log ( ) log ( )
22 2min
log log 1 2 log
In Q n
env
rn A Qn E B
−
⎡⎤
⎛⎞
=⋅ + + − +
⎢⎥ ⎜⎟
⎝⎠ ⎣⎦
(3−8)
56
where A is a logarithmic-compression constant and can be expressed as
2
20 255
log (10)
A
DR
×
=
⋅
(3−9)
Figure 3-1 shows the conceptual block diagram of the proposed design
expressed by Equation (3-8) except the gain factor B for the sake of simplicity. The
fixed-point numbers of both ( ) In and ( ) Qn are converted to the binary logarithmic
numbers through LUT depicted by two bold boxes containing base 2 logarithmic
values represented by BLNS in Figure 3-1. The result of a simple subtraction of
()
BLNS
In and ()
BLNS
Qn is used as an input address to determine the output of LUT,
which is a square root value expressed in the second term of Equation (3-2). Once a
dynamic range of enveloped echo signal is determined, the minimum envelope value
Figure 3-1: Conceptual block diagram of the proposed design. A is a logarithmic
compression constant and ( )
2min
log E is the weakest envelope value in
logarithmic scale. Three bold boxes represent the look-up tables: two for the
conversion from the fixed-point numbers to binary logarithmic numbers and one
for the square root function.
57
in logarithmic scale is subtracted from the result of a simple addition between the
output of LUT for square root function and the quadrature component ( )
BLNS
Qn .
Finally, the logarithmic-compressed envelope information is obtained by multiplying
the subtraction results by the logarithmic-compression constant. Although the gain
factor B is not shown in Figure 3-1, in addition, the system gain including one of
LPFs can be compensated by adding B to the logarithmic-compressed envelope
information obtained. The conceptual block diagram can be implemented with
hardware logic components as shown in Figure 3-2 including remedies for
logarithmic representation of zero number and boundary detection.
If in-phase and quadrature components are represented by m-bit fixed-point
numbers and converted to k-bit binary logarithmic numbers, two 2
m
k × -bits memory
Figure 3-2: Hardware logic description to extract the logarithmic-compressed
envelope information from the baseband components represented by a m-bit
fixed-point number system, which is converted to a k-bit binary logarithmic
number through LUT
A
. And the square root values are generated through LUT
B
.
The proposed envelope detector generates 8-bit resultant data going to a digital
scan converter in which gray-level images are displayed on a monitor.
58
for converting fixed-point numbers to binary logarithmic numbers (LUT
A
) and one
1
2
k
k
+
× -bit memory for the square root value (LUT
B
) are used as shown in Figure 3-
2. Each hardware logic component has latency of one clock cycle except LUTs and
boundary detectors of which latency is two clock cycles. Therefore, the latency for
the square root function including logarithmic compression becomes 15 clock cycles.
The latency for the quadrature demodulation depends on the number of taps required
for a LPF. If a 33-tap LPF is used to obtain a complex baseband component,
outcomes from the LPF after 16 clock cycles ( (33 1) 2 − ÷ ) can be regarded as a valid
output set to maintain the same number of input and output samples although it still
contains transient output data. In this case, the latency for the quadrature
demodulation is 17 clock cycles including latency of one clock cycle for mixing echo
signals with sine and cosine waveforms. As a result, the total latency of the proposed
design is 32 clock cycles, so that a logarithmic-compressed envelope sample can be
obtained at every clock cycle after 32 clock cycles.
By a maximum error analysis, the minimum number of bits representing binary
logarithmic numbers can be determined so as to avoid the rounding error. The error
of the proposed design arises from the conversion of baseband echo signals into
binary logarithmic numbers to carry out the fast square root computation and
logarithmic compression. If a logarithmic number is represented by I-bit integer and
F-bit fractional parts, the maximum conversion error is
( ) 1
2
F − +
and thus both a
subtraction and an addition of two binary logarithmic numbers generate the
maximum error of 2
F −
. Since the outcome from the second term of Equation (3-2)
59
can be exactly calculated by a computer and stored in LUT
B
with
() 1
2
F −+
error, its
maximum error is still equal to 2
F −
arising from the subtraction of () ()
2
log In and
() ()
2
log Qn . As a result, the maximum error of the proposed design can be
expressed as
() ( ) [ ] ()
{}
() ( )
max max 2 2 min
1
max max max
1
max max
log log
22 2
2222
B
FF F
FF
err A err Q n err LUT err E
AA A
AA
β
β
−+ −+ −
−−−−
⎡⎤ =⋅ + + ⎡ ⎤
⎣ ⎦ ⎣⎦
=⋅ + ⋅ + ⋅
⎡⎤ =⋅ + ⋅ ⋅ +
⎣⎦
(3−10)
where [] err is a function for computing the maximum error, β is the number of
extra fractional bits assigned to
min
E in BLNS, and
max
A is a possible maximum
integer value of the logarithmic compression constant. If DR is greater than or equal
to 48 dB,
max
A becomes 32 (
5
2 ) and thus Equation (3-10) can be rewritten by
55 1
max
22 2 2
FF
err
β −+ −+ − −
⎡ ⎤ =+ ⋅ +
⎣ ⎦
(3−11)
If β is greater than 1 and F is greater than 7, the maximum error is always less
than 0.5, i.e., within the rounding error. Since the maximum error analysis tends to
overestimate the error of a system, the number of bits of the fractional part in BLNS
can be assigned to 6 instead of 7 in spite of the maximum error of 0.875 which rarely
occurs.
The number of bits of the integer part in BLNS, I, is determined by the number
of bits used to represent fixed-point numbers, i.e., ( )
2
log number of bits ceil ⎡ ⎤
⎣ ⎦
where
a function of [] ceil returns the smallest integer value no less than its input value. If
60
() In and ( ) Qn in Equation (2-11) are represented by the 16-bit fixed-point number
system, therefore, the number of bits of integer and fractional parts in BLNS is 4 bits
and 6 bits, respectively. A Total of bits for BLNS become 10 bits. From this result,
the memory size for the conversion is 164 Kbytes (
16
22 10 8 × ×÷ ) and it for square
root function generating 10-bit outcomes is 2.56 Kbytes (
11
210 8 × ÷ ) considering a
sign bit resulting from the subtraction. Therefore, a total of 166.56 Kbytes memories
are used for the proposed design. This memory size is noticeably reduced, compared
with a 4 Gbytes (
32
288 ×÷ ) size of memory in the fixed-point number system.
Through the change of the number system, furthermore, the logarithmic compression
functional block can be removed and merged with the proposed envelope detector.
3.3 Experimental Results
The validation of the proposed design was achieved by comparing its outcome
with that of the conventional quadrature demodulation method using MATLAB. For
the sake of comparison, the envelope information of the conventional quadrature
demodulation shown in Figure 2-7 was logarithmically compressed to a 48 dB
dynamic range. The proposed design employed the same LPFs and sine/cosine data
as those used for the conventional quadrature demodulation in Section 2.2.4. The
total number of bits for BLNS was 10 consisting of a 4-bit integer part and a 6-bit
fractional part, where the word sign bit was removed because only the magnitude of
61
each the complex baseband component contributes to obtaining the envelope
information. Figure 3-3 shows the logarithmic-compressed envelope data represented
by 8-bit gray level obtained by the conventional quadrature demodulation (gray solid
line) and the proposed method (dotted line) adopting 10-bit BLNS. The maximum
difference between the two methods was 0.476, which was within the rounding error.
Once the fractional part of BLNS was assigned to 7 bits so as to make 11-bit BLNS,
Figure 3-3: Comparison of accuracy of the proposed design (dots) with that of the
conventional quadrature demodulation method (gray solid line).
62
the maximum difference was reduced to 0.237. In addition, the normalized RMSE of
the proposed design with 10-bit BLNS and logarithmic-compressed version of the
ideal Hilbert transformer shown in Section II was 7.472 %, which was less than that
of the conventional quadrature demodulation with ideal logarithmic compression, i.e.,
7.473 %. In fact, logarithmic compression may increase the normalized RMSE value
of a certain system. From the results, it is seen that the proposed envelope detector is
capable of providing the same functionality as the conventional quadrature
demodulation with negligible quantization error, i.e., within rounding error.
The hardware implementation of the proposed design shown in Figure 3-2 was
carried out in a FPGA (Stratix EP1S60F1020C6, Altera Corporation, San Jose, CA)
on a test board operating at 100 MHz. The specifications in the hardware
implementation were the same as those for MATLAB simulation except for the echo
signal. A single scan vector consisting of 8-bit 2048 samples was obtained from a
rabbit eyeball with a 20-MHz single element transducer as shown in top panel of
Figure 3-4. The single scan vector was stored in the FPGA internal memory to
calculate the operating time of the proposed design. Whenever an external trigger
signal comes into the test board, the memory containing the single scan vector starts
to send the stored data to the envelope detector module, which starts its task by the
external trigger signal as well. Theoretically, a total of 2080 clock cycles including
32 clock cycle latency are needed to perform the envelope detection for the single
scan vector, so that the fastest triggering frequency should be around 48.1 KHz at
100 MHz clock frequency. In the experiment, as expected, the highest triggering
63
Figure 3-4: logarithmic-compressed envelope information extracted by the
proposed design implemented in FPGA (dots in bottom panel). The resultant
envelope shape from the proposed design is compared to those of the ideal
Hilbert transformer (gray solid line in bottom panel) and the conventional
quadrature demodulation (dashed line) obtained on MATLAB. Top panel shows
a single scan vector acquired from a rabbit eyeball obtained by a 20-MHz single
element transducer.
64
frequency was 48 KHz corresponding to a 20.8 s μ operating time needed to extract
the envelope information from the echo signal comprising of 2048 samples. If a
frame consists of 256 scanlines, the total time to obtain logarithmic-compressed
envelope samples of a frame is 5.3 ms in the proposed design, thus satisfying the
requirement of the processing time. As a result, it is shown that the proposed design
can be used for very high frame rate high frequency ultrasound system generating
more than 100 frames per second.
In the bottom panel of Figure 3-4, it is shown that the logarithmic-compressed
envelope extracted by the proposed design in hardware (dots) is the same as that by
the conventional quadrature demodulation (dashed line) obtained from MATLAB
simulation. The maximum error of the proposed design compared with the
conventional quadrature demodulation with ideal logarithmic compression was 0.465,
which can be negligible in practice. In addition, the normalized RMSE between the
envelope data of the proposed design and the ideal Hilbert transformer obtained from
MATLAB simulation (gray solid line in the bottom panel of Figure 3-4) was
5.177 %, which was similar to that of the conventional quadrature demodulation.
Because the low pass filtering in the quadrature demodulation discards high
frequency components of the original echo signal, the fluctuated portion on the
logarithmic-compressed envelope signal from the ideal Hilbert transformer becomes
smoother. In B-mode image, however, this phenomenon should not affect much the
image quality because meaningful information such as tissue structures can be still
obtained from the overall shape of the envelope signal. This can be confirmed by B-
65
mode images of a formalinized pig eyeball shown in Figure 3-5.
The formalinized pig eyeball was linearly scanned by using an ultrasound
biomicroscope (UBM) system with a 50-MHz signal element transducer which has a
-6 dB bandwidth of 55 % and a focal distance of 6 mm (1.4 f-number). Echo signals
were sampled by using 14-bit ADC (CS14200, Gage Applied Technologies,
Montreal, Quebec, Canada) at 200 MHz. A frame was composed of 400 scanlines
and 2048 samples per scanline. And envelope information was logarithmically
compressed to a 60 dB dynamic range. The image produced by the proposed design
shown in Figure 3-5 provides information about the anterior segment of the eye such
as the cornea, the iris, and the lens as clearly as that by the ideal Hilbert transformer
shown in Figure 3-6.
3.4 Conclusions
A high frame rate high frequency ultrasound imaging system requires not only
very fast data acquisition but also fast signal processing to generate images in real
time. This Chapter has proposed a novel design of envelope detectors capable of
supporting the small animal cardiac imaging system requiring very high frame rate
(more than 100 frames per second). To achieve very fast operating speed as well as
good accuracy, a new way that uses LUT for obtaining the square root function by
computing the magnitude of the complex baseband components extracted from the
66
quadrature demodulation is proposed. The new LUT strategy with BLNS has the
advantage of reducing the size of LUT, thus enabling us to take full advantage of the
attractive properties of the LUT method which allow a fast operating speed, high
accuracy, and simple implementation. The performance of the proposed design was
examined and the results have shown that the proposed design is suitable for
Figure 3-5: B-mode image of the excised pig eyeball involving the proposed
design. The images have a 60-dB dynamic range and its focal depth is 6 mm.
67
envelope detection in a high frame rate high frequency ultrasound imaging system in
terms of operating speed and accuracy. Since being capable of providing
logarithmic-compressed envelope data at the same rate of sampling clock of systems,
especially, the proposed design enables us to use linear interpolation algorithm for
DSC with an acceptable accuracy as discussed in Section 2.4.1.
Figure 3-6: B-mode image of the excised pig eyeball involving the ideal Hilbert
transformer. The images have a 60-dB dynamic range and its focal depth is 6 mm.
68
CHAPTER 4
DESIGN OF HIGH FRAME RATE DIGITAL SCAN CONVERTER
FOR HIGH FREQUENCY ULTRASOUND SECTOR SCANNER
4.1 Introduction
For the purpose of the cardiac imaging requiring a system to adequately
capture its fast movement, high-speed scanning can be effectively realized with a
phased array transducer. Unfortunately, the phased array transducer for high
frequency ultrasound imaging is currently not available due to the difficulty of
fabricating its array elements with a small pitch to avoid grating lobes as mentioned
in Chapter 1. Therefore, several researchers have proposed the alternative ways to
image the mouse heart. One is to use a linear array transducer at the expense of a
narrow view width (Xu et al., 2005). High-speed scanning with a enough field of
view can be achieved by mechanical sector scanning with a single element
transducer. In order to do so, sophisticated motor controlling is necessary and
recently a mechanical sector scanner capable of acquiring 130 frames per second
with a view angle of 22 degrees has been reported (Sun et al., 2007). The other
proposal is a scanning method triggered by the echocardiography (ECG) signals of
the mouse for the very fast data acquisition, i.e., up to 10,000 frames per second
(Chérin et al., 2006; Liu et al., 2006). This technique can provide the detailed
69
information of cardiac activity under the condition where the heart regularly pulsates.
However, abnormal heart rhythms arising from arrhythmia make it difficult to form
the images with pre-acquired echo data, thus restricting the use of the technique to
diagnose the pathology of the heart.
In the sector scanning using either a phased array or a single element
transducer, the locations of echo samples acquired within imaging plane and pixels
on a monitor are not the same; the echo samples are in a polar coordinate system and
the pixels are in a Cartesian coordinate system. Because the samples are acquired in
a polar coordinate, in addition, the population of the echo samples in a unit imaging
area will decline as the imaging depth (i.e., the radii of samples in the polar
coordinate) increases. For this reason, the direct mapping of the echo samples onto
the pixels usually causes the Moiré artifact. In sector scanning using either a phased
array or a single element transducer, therefore, a digital scan converter (DSC) is a
pivotal element, which performs interpolation to find appropriate pixel value with
the small population of the echo samples.
A DSC typically consists of four functional blocks: a pixel address generator, a
coordinate transformer, an interpolator, and a display memory block. Each pixel
constituting an image is typically assigned a unique address in a Cartesian coordinate.
The pixel address generator is responsible for sending the assigned addresses to the
coordinate transformer and the display memory block. The coordinate transformer
converts the pixel addresses into the corresponding locations in a polar coordinate; it
generates radii and angles of the pixels for data interpolation. The radius of a pixel is
70
used to select the echo samples either surrounding a target pixel for the bilinear
interpolation algorithm or being the nearest to the pixel for the linear interpolation
algorithm. In case of the bilinear interpolation algorithm, the coordinate transformer
is also responsible for generating radial differences between a target pixel and the
selected samples for the radial interpolation after the selection of echo samples. It
should be noted that the linear interpolation does not require this step. In order to
provide the interpolator with the echo sample values selected, the coordinate
transformer converts the radius information of the pixels to the corresponding
addresses of a buffer responsible for containing the logarithmic-compressed echo
samples obtained along a scanline, which is called line buffer in this work. For the
angular interpolation, the coordinate transformer uses the angle information of the
pixels to generate angular differences between a target pixel and the selected samples.
With the information generated by the coordinate transformer, the interpolator
calculates target pixel values using either Equation (2-13) and Equation (2-14) for
bilinear interpolation or Equation (2-15) for linear interpolation. The results of the
calculation are finally stored in the display memory block.
In order to obtain more than 100 images a second for the cardiac imaging of the
mouse, the entire processes mentioned above should be completed within less than
10 ms. If an image consists of 262,144 pixels (512 by 512 image size), about 38 ns
(10 ms divided by 262,144) is available to carry out the entire scan conversion
process for a pixel. This time corresponds to 3 clock cycles at 100 MHz operating
clock frequency. This requirement for fast operating speed is a challenge because a
71
very fast computational speed and wide bandwidth of data transfer between each
functional block are required. Software-based implementation using a commercial
media processor (Sikdar et al., 2001) is currently incapable of satisfying the
requirement because these processors do not have enough computational power and
data transfer bandwidth to realize a high frame rate imaging system. The best
performance is currently 31.3 clock cycles for a pixel, in which 8.7 cycles and 22.6
cycles are used for interpolation and data transfer between external memories and
internal memories, respectively. Therefore, the hardware-based implementation of
DSC is the only possible approach although it requires a high-cost sophisticated
design due to its fast operating speed.
In this Chapter, the hardware-based implementation of DSC for high frame rate
cardiac imaging involving sector scanning is described. In order to achieve the
desired processing speed, the designed DSC employs LUT based coordinate
transformation and the linear interpolation algorithm in which two nearest samples to
each object image pixel are selected and an angular interpolation is performed as
described in Section 2.4. The design focuses on the efficient use of LUT to
implement DSC in a single field programmable gate array (FPGA) as well as high
speed data transfer between each functional block.
4.2 Overview of DSC Work Flow
72
In order to perform coordinate transformation, each pixel constituting an image
is assigned a unique address in a Cartesian coordinate as shown in Figure 4-1, which
is an example of pixel addressing of 256-by-256 sized image. Eight most significant
bits correspond to a location in X-axis whereas the other bits a location in Y-axis. So
the total number of bits representing pixel addresses are 16. For instance,
hexadecimal 0x8000 in Figure 4-1 is composed of 0x80 for a X-axis location and
0x00 for a Y-axis location. The reference column in the figure indicates the center in
X-axis. An interesting feature in this form of addressing is that X-axis components of
Figure 4-1: Configuration of pixel addressing of 256 by 256 sized image. The
reference column indicates the center in X-axis.
73
two different pixels at equal distances from the reference column are two’s
complement to each other. In Figure 4-1, for example, X-axis components of 0x7F00
and 0x8100 are two’s complement, i.e. 0x100-0x7F=0x81. By using this feature, the
size of LUT for coordinate transformation can be reduced to approximately half.
The addressed pixels belong to each sector scan slice formed by two adjacent
scanlines as shown in Figure 4-2. Therefore, scan conversion process for pixels
within a sector scan slice can start after storing echo samples from the two scanlines
forming the slice. In Figure 4-2, for example, scanline
0
SL and
1
SL form the slice
colored gray, so that the scan conversion for pixels within the slice is performed with
echo samples acquired from the two scanlines and stored in two line buffers while
echo samples from
2
SL is being stored in other line buffer. This conversion scheme
Figure 4-2: Sector scan slice colored gray formed by two adjacent scanlines, i.e.,
0
SL and
1
SL . Scan conversion for pixels within the slice is performed with stored
samples from the two scanlines while echo samples from
2
SL is being stored.
74
requires only three small-size memory blocks, i.e., line buffers ( 3 Nk ×× bits) to
store echo samples corresponding to three scanlines instead of a large-size memory
( SN N k ×× bits) to store the entire samples of a frame, where N is the number of
samples in a scanline, k is the number of bits representing a sample, and SN is the
number of scanlines.
Figure 4-3 shows a timing diagram describing DSC work flow when the
number of scanlines is 8 as an example. A scanline start (SL_START) signal comes
from an envelope detection module to indicate that logarithmic-compressed echo
samples acquired from a scanline are available to store. This signal is synchronized
with a PRF trigger signal indicating that a transducer is excited, which comes from a
front-end system. Whenever the SL_START signal is issued, the scanline number
(SL_NUM) is increased by one. Once SL_NUM reaches zero, a signal indicating a
Figure 4-3: Timing diagram describing DSC work flow when the number of
scanlines is 8 as an example. Start and end point of each arrow represent cause
and effect signals, respectively.
75
new frame (NEW_FRAME) is generated. A first-line-buffer-write-enable signal
(LB_WR_0) generated by the NEW_FRAME signal causes the first line buffer to
start to store logarithmic-compressed echo samples. LB_WR_1 and LB_WR_2 for
the second and the third line buffers are generated by the next SL_START signals in
their turn. These signals for line buffers are issued in consecutive order until the
NEW_FRAME signal is triggered again. When SL_NUM becomes two, it generates
a scan-conversion-start (SC_START) signal to trigger scan conversion process for a
frame. The scan conversion starts with generating a left scanline number (LEFT_SL)
standing for a sector scan slice. For example,
0
SL stands for the gray sector scan
slice in Figure 4-2 because it is located on the left side of the slice. The pixel address
generator provides pixel addresses within the slice indicated by the LEFT_SL value
both to a coordinate transformer to perform data interpolation and a display memory
block to store scan converted pixel values.
4.3 System Description
The designed DSC block consists of a pixel address generator (PAG), a line-
buffer-read-address generator (LBRAG), a fractional angle generator, and three line
buffers as shown in Figure 4-4. In order to achieve the desired operating speed,
LBRAG and the fractional angle generator responsible for coordinate transformation
are implemented by a LUT method with the symmetry property of a sector scan
76
image that enables us to save the size of LUT.
4.3.1 Pixel Address Generator
The generation of pixel addresses corresponding to a given sector scan slice
can be also realized by a LUT method. Each pixel belongs to only one among sector
scan slices, and the number of pixels within a given sector slice is determined by
several factors: number of scalines, view angle of imaging plane, imaging depth, and
number of pixels in an image. Once these factors are determined, we can determine
which pixels belong to which sector scan slices, so that the space of LUT can be
divided by the number of the slices constituting an imaging plane and the each space
contains the addresses of pixels within the corresponding slice. With LEFT_SL
values indicating each slice, therefore, PAG sends the addresses of pixels within
current sector scan slice to LBRAG and a display memory block.
Figure 4-4: Functional block diagram of designed digital scan converter.
77
However, the direct realization of the LUT method requires a large size of
memory, i.e., () ( )
2
1log
x y
NM KK −× × × bits, where N is the number of scanlines,
M is the maximum number of pixels within a given sector scan slice, and
x y
KK ×
is the image size. For the case of a 512 by 512 image and 200 scanlines, for example,
the memory size should be 4.7 Mbits where M is obtained by the calculation
(512×512÷200). For fast frame rate systems, it is difficult to use an external memory
like SRAM and SDRAM as LUT because this requires not only complicated control
logics, but also a very efficient layout of external buses on PCB with robust noise
tolerance. Especially, SDRAM commonly used for an external memory due to the
high density of memory cell with low cost can be hardly used as LUT for the high-
speed DSC. This is so because it is a large time consumer due to the latency from
SDRAM row misses frequently generated in DSC. Sikdar et al. (2001, 2003) pointed
out that fetching entries of LUT from an external memory (i.e., SDRAM) consumes
about 72 percent of the total operating time of DSC for an image. Therefore, LUT
should be implemented with the internal memory of FPGA, so that the memory size
of 4.7 Mbits for EPA is too big to be implemented in it.
In order to overcome the problem, the proposed design performs the function
of encoding the pixel addresses. Each pixel within a given sector scan slice, called an
effective pixel group in this design, is vertically subdivided into
0
G to
7
G indicated
by dotted rectangles in Figure 4-5. Each subgroup has a leading pixel represented by
dotted circles. It should be noted that a pixel address in a subgroup can be calculated
78
Figure 4-5: Description of grouping effective pixels and linear interpolation
within two adjacent scanlines
i
SL and
1 i
SL
+
indicated by bold dashed lines. A
multiplication sign represents an image pixel. A dotted rectangle represents one
of subgroups of the effective pixel group within the two scanlines. A dotted circle
designates a leading pixel in each subgroup. Filled circles on the scanlines
represent acquired samples. The multiplication sign in a diamond is an object
effective pixel to linear interpolation. α and β are angular differences between
P and
i
SL and
1 i
SL
+
.
79
with a leading pixel address and the position number of the object pixel in the
subgroup. For example, the address of the object pixel P in subgroup
4
G is obtained
by adding its position number 6 to the Y-axis component of the leading pixel address
40 XY , so that the address becomes 46 XY . Therefore, both effective pixel group
numbers identified by LEFT_SL values and subgroup numbers within each effective
pixel group can be used as indices of LUT. Each entry of LUT for the indices
contains a leading pixel address of a subgroup and the number of members of the
subgroup. The memory size for this LUT strategy is therefore
() ()
2
Memory Size (bits)= 1 log
2
x
x yy
K
NKKK −× × × × (4−1)
Under the previous condition, the memory size for LUT is reduced from 4.7 Mbits to
1.4 Mbits. Figure 4-6 shows an example describing the contents of LUT and its
output value for the sector scan slice in Figure 4-5. The number of LUT indices is
eight because there are eight subgroups. Each entry corresponding to the indices
contains a leading pixel address and the number of a subgroup member. For the
second index representing subgroup
1
G , its entry contains the leading pixel address
16 XY and four, which is the number of
1
G member.
PAG is responsible for fetching the subgroup information from LUT and
retrieving the information to generate addresses of its member pixels. Figure 4-7
shows a hardware logic description of PAG and Figure 4-8 is a flow chart explaining
the functionality of a controller in the hardware logic description. Once a LEFT_SL
value is updated by the SL_START signal, the index of LUT starts with the updated
80
value of LEFT_SL and subgroup 0,
0
G . The controller waits for an effective-pixel-
address-request (EPA_REQ) signal coming from DSC control logic while the entry
of LUT corresponding to the index is appearing at its output port. If the first
EPA_REQ signal is issued, X-axis and Y-axis components and the number of the
subgroup member (#SGM) of the current entry are loaded into a D-type flip flop
(DFF), an upward counter (UP_CNT), and a downward counter (DOWN_CNT),
Figure 4-6: An example to describe the contents of LUT and its output value. Left
scanline number
i
SL and a subgroup number constitute an index of LUT. For the
sector scan slice in Figure 4-5, the number of indices is eight because there are
eight subgroups. Each entry corresponding to the indices contains a leading pixel
address and the number of a subgroup member. In case of the second index
representing subgroup
1
G , its entry contains the leading pixel address 16 XY and
number four. Its outputs are generated by increasing a leading pixel address by
one as many as the number of a subgroup member minus one.
81
respectively. After one clock cycle, PAG can provide a pixel address, and the index
of LUT is increased by one so that the entry corresponding to the current LEFT_SL
value and subgroup 1,
1
G , can appear at the output port. When the next EPA_REQ
signal is generated, the controller checks whether or not the number of the current
subgroup member is one. If it is not one, Y-axis component is increased by one so as
to change the current pixel address and #SGM is decreased by one. This procedure
continues until #SGM becomes one. Once #SGM becomes one, DFF and counters
loads the next group information already generated at the output port of LUT. In the
designed DSC, PAG is the main time bottleneck, which spends 3 clock cycles to
Figure 4-7: Hardware logic description of a pixel address generator (PAG). DFF
is a D-type flip flop, UP_CNT is an upward counter, and DOWN_ CNT is a
downward counter.
82
generate a pixel address.
4,3.2 Coordinate Transformer and Interpolator
Figure 4-8: Flow chart to explain the functionality of PAG. #SGM is the number
of a subgroup member and REQ and GN stands for request and generation,
respectively.
83
A pixel address provided by PAG is sent to LBRAG and the fractional angle
generator to perform coordinate transformation and linear interpolation. The two
functional blocks can be straightforwardly implemented by the LUT method. Indices
of LUTs belonging to the two functional blocks are pixel addresses in the reference
column and its left side in Figure 4-1. Pixel addresses in the right side of the
reference column are converted into two’s complement forms to obtain their
corresponding values from the entries for their equal distance pixel addresses on the
left of the image plane. Entry values of the LUTs are computed in a personal
computer (PC) and loaded into the LUTs.
Linear interpolated value
P
A of a pixel P is obtained by the following as
shown in Chapter 2:
12
P
SS
A
α β
αβ
× +×
=
+
(4−2)
where
1
S and
2
S are two nearest samples to P along radius direction and α and β
are angular differences between P and the two selected samples as shown in Figure
4-5. LBRAG plays a role in providing the line buffers with the sample address
corresponding to a given pixel address to make the line buffers send the two samples
to the interpolator. Entries of LUT in LBRAG can be calculated by
()
2
2
Sample Address
jC j
sample
dX X Y
round
⎛⎞
Δ⋅ − +
⎜⎟
=
⎜⎟
Δ
⎜⎟
⎝⎠
(4−3)
84
where
j
X and
j
Y represent a X-axis and Y-axis address components of the j-th pixel
and
C
X is a X-axis address component of the reference column corresponding to
origin in the Cartesian coordinate. d Δ is a distance between two successive pixels in
horizontal or vertical directions,
smaple
Δ is a sample interval, and ( ) round is a
function producing the nearest integer value. Note that the two sample values
1
S and
2
S in Equation (4-2) are located at the same address of two different line buffers.
The fractional angle generator has LUT in which entries are β values in
Equation (4-2). If the angle of i-th scanline is
SLi
θ and the angular difference
between
i
SL and
1 i
SL
+
is predetermined value θ Δ , β can be obtained by
1
tan
i
jC
SL
j
XX
Y
βθ
−
⎛⎞ −
=−
⎜⎟
⎜⎟
⎝⎠
(4−4)
And α can be simply calculated by
α θβ =Δ− (4−5)
Therefore, the fractional angle generator consists of LUT containing precomputed β
and a subtractor to calculate α . With the values generated by the coordinate
transformer and the line buffers, the interpolator computes an object pixel value
using Equation (4-2).
85
CHAPTER 5
HIGH SPEED BACK-END PROCESSING SYSTEM
FOR MECHANICAL SECTOR SCANNER
5.1 Mechanical Sector Scanner
The back-end subsystem was tested on a mechanical sector scanner which
acquires echo signals in a fan-shaped imaging plane by mechanically moving a
single element or annular array transducer along an arc line as shown in Figure 1-2
(b). In order to do so, the implementation of the mechanical sector scanner mainly
focuses on motor control performed by the servo motor controller in Figure 5-1. The
servo motor controller is realized by a closed loop proportional-integral-derivative
(PID) algorithm through which the position signal of a servo motor keeps tracking a
predetermined reference waveform. The closed loop PID algorithm can relieve the
problem of nonlinear motor position along time resulting from frequently
decelerating and accelerating the motor, thus carrying out uniform spatial sampling
at a high swing rate. The servo motor controller not only adjusts motor drive power
to eliminate the differences between the current motor position and a reference
waveform but also provides the current motor position to the PRF trigger generator.
The input waveform to the PRF trigger generator is shown in Figure 5-2. The
positive slope of the position signal means that a motor is moving away from a start
86
Figure 5-2: Scheme of generating PRF trigger signals based on a given motor
position signal from the servo motor controller.
Figure 5-1: Functional block diagram of a front-end system of a mechanical
sector scanner.
87
position referred to as zero degree, which is called forward swing. The motor is
moving back to the start point in its negative slope, which is called backward swing.
At the zero voltage level of the position signal, the surface of a motor is in parallel
with the surface of a subject. The PRF trigger generator produces a PRF trigger
signal at a predetermined voltage level of the position signal. The pulse generator
creates a high electric voltage to excite a transducer whenever a PRF trigger signal
comes in. An expander plays a role of eliminating noise from the pulse generator on
transmit and decoupling the pulse generator from a preamplifier on receive. On the
other hand, a limiter protects pulse receive circuits from the high electric voltage on
transmit event and passes echo signals to a preamplifier to boost up the level of the
signals on receive. The preamplifier can involve a band pass filter (BPF) to improve
signal-to-noise ratio (SNR) by suppressing noise outside the desired bandwidth of
echo signals to a certain level. The mechanical sector scanner provides the PRF
trigger signals and the amplified echo signals to a back-end processing system.
Recently, the NIH Resource Center for Medical Ultrasound Transducer Technology
at the University of Southern California and Capistrano Labs (San Clemente, CA)
have developed a mechanical sector scanner capable of providing about 65 frames
per second with a view angle of 22 degrees in forward swing.
5.2 Back-end Processing System for B-Mode Imaging
88
Figure 5-3 shows the overall system block diagram of the designed back-end
processing system for B-mode imaging. The system can be classified into a host
processor and a periphery. The host processing block as shown by bold outlined box
in Figure 5-3 is responsible for image display and a user interface, which are
implemented by software programs written in C++. The peripheral block indicated
by dashed box performs DC cancelling, digital time gain compensation (DTGC),
envelope detection including LOG compression, digital scan conversion (DSC), and
controlling peripheral component interconnect (PCI) bus on master mode, which is
implemented in a single FPGA (Stratix EP1S60F1020C6, Alteral Corporation, San
Jose, CA).
Echo signals coming from the scanner are sampled by an 12-bit analog-to-
Figure 5-3: Overall system block diagram of designed back-end processing
system for B-mode imaging.
89
digital converter (ADC) (AD9430, Analog Devices Inc., Norwood, MA) at 200 MHz
and sent to DSC board via a low voltage differential signaling (LVDS) bus that is a
suitable method to send out digital data at a very high rate (more than 100 Mbps).
The digitized echo samples contain the certain level of a DC component imposed by
an amplifier and ADC. The DC canceller removes the DC component to provide an
envelope detector with zero-offset echo samples. The DTGC logic digitally
compensates for the attenuation of ultrasound along axial direction. In the envelope
detection logic block, the envelope detector combined LOG compressor developed
carries out extracting LOG-compressed envelope information from the echo samples
synchronized with the 200-MHz clock provided by the ADC board. Once the first
two line buffers are filled with the samples, the DSC developed starts the conversion
process and stores pixel values into one of two on-chip display memory banks,
where each memory bank is capable of storing 65,536 pixel data (256 by 256 image
size) corresponding to an image. For the sake of efficient data transfer to PC, the one
memory bank stores scan converted pixel values while the data in another memory
bank is sent to PC through 64-bit 33-MHz PCI bus.
A user interface module handles a high performance video card (RADEON
9800 PRO, ATL Corporation, MD) by using OpenGL API which is a standard
graphic application programming interface (API) to control a video card made by
different vendors. OpenGL allows using a texture mapping method for enlarging
scan converted images to the desired size with minimal computational power. In
addition, the user interface module is responsible for storing the image data into a
90
hard disk of PC with a time stamp containing PC clock time when an image data is
completely stored in PC memory. One thousand successive images can be stored in a
hard disk of PC.
5.2.1 DC Canceller
Noise in ultrasound imaging systems is generated by a transducer as well as
electronic components. The noise from a transducer is associated with thermal noise
sources of the transducer itself and acoustic loads, and its noise figure has much
larger value in frequencies outside the passband of the transducer than inside because
of the bandpass property of transducers (Rhyne, 1998). And this noise figure
becomes worse at the output port of preamplifiers. In addition, electronic
components in the system always generate various types of noises such as thermal
noise, shot noise, flicker (or 1 f ) noise, and burst noise. The thermal and shot noises
have the same property as white noise of which the power spectral density is
constant over all frequency range. On the other hand, the flicker and burst noises
mainly affect signals in the low frequency range, thus causing the degradation of
preamplifier performance due to input offset voltage created by the noises.
Echo signals are distorted by these noises mentioned above that are time-
variant low-frequency signals; the power spectrum of the noise signal has large value
around zero frequency (or DC component of frequency). Figure 5-4 shows an A-line
91
signal extremely distorted by the noises (dashed line). It is seen from the figure that
the A-line signal is loaded onto a low frequency signal that results from the noises.
From this noisy signal, an envelope detector cannot extract correct envelope
information. So that ultrasound imaging systems should employ a DC canceller
responsible for removing the low frequency noise signal. The simplest method for
the DC cancelling is the use of a high pass filter (or a band pass filter), optimally
designed to suppress the DC component of a noisy signal below al least -60 dB
Figure 5-4: Result of a DC canceller implemented using a high pass filter. The
dashed line shows an A-line signal distorted by various types of noises and the
solid line is the resultant signal of removing the noises from the A-line signal in a
DC canceller.
92
without the distortion of the main signal. The solid line in Figure 5-4 is the resultant
A-line signal from the DC canceller designed using a high pass filter.
5.2.2 Digital Time Gain Compensator
Ultrasound pressure exponentially decreases as ultrasound travels through the
body due to both absorption and scattering of ultrasound energy as shown in
Equation (1-3). Therefore, meaningful echo signals from reflectors in between near
and far positions from a transducer have a large dynamic range (more than 100 dB).
This dynamic range cannot be efficiently displayed on a monitor because of not only
the limited capability of the monitor, but the performance of ADC. In order to
overcome the problem, common ultrasound imaging systems employ an analog time
gain compensator before ADC and/or a digital counterpart after ADC (Richard,
1989; Pye et al., 1992; Foster and Wheeler, 1996).
In this work, a digital time gain compensator with capability of cooperating
with an analog counterpart was implemented. Figure 5-5 illustrates its hardware
logic description capable of increasing the level of echo signals by the range of 0 to
30 dB. In the implementation, the imaging depth is divided by 8 partial areas and
users can set an overall gain for the entire imaging area and increments from the
overall gain for the partial areas in a graphic user interface. With the parameters set
by users, the host processor computes the gains of TGC for each echo sample
93
constituting a scanline and stores the gains in a 2048 15-bit word RAM in Figure 5-5.
As shown in the figure, the each gain value, in linear scale instead of decibel scale, is
represented by an unsigned 15-bit fixed-point number that has a 5-bit integer part
and a 10-bit fractional part; the maximum value represented with this number of bits
is 31.999 corresponding to about 30.1 dB. After multiplying a gain value and an echo
sample represented by a singed 12-bit fixed-point number, we can obtain a result
consisting of a sign bit, a 16-bit integer part, and a 10-bit fractional part. The upper
17 bits of the result is a compensated echo sample value that can be obtained by a
division calculation. For consistency with the number of bits of an echo sample, 12
bits out of 17 bits of the result is chosen and users can determine which bits will be
selected through setting up the Cutting Bits register. If all 5 output bits of the register
are 0, for example, the R-Shifter & Saturation Detector logic chooses 12 right-most
bits out of the 17 bits as a resultant echo sample value. And if the most significant bit
Figure 5-5: Hardware logic description of the digital time gain compensator
implemented in this work.
94
of the output of the register is set to 1, the sample value will be 12 left-most bits out
of the 17 bits. The control logic in the figure is responsible for storing corresponding
data to either RAM or the Cutting Bits register and serves as a manager for making
the RAM send out the gain values along with the acquisition time of echo signals.
Figure 5-6 and 5-7 show the results of verifying the functionality of the time gain
compensator developed here.
40-MHz sinusoidal signals with the peak-to-peak voltage of 100 mV were
provided to the back-end processing system developed here. At first, the LOG-
Figure 5-6: Results of verifying the functionality of the implemented digital time
gain compensator. The back-end processing system developed produced images
from 40-MHz sinusoidal signals with the peak-to-peak voltage of 100 mV that
were provided by a function generator. The left panel is a resultant image without
involving DTGC. On the contrary, the right panel is an image with DTGC. The
middle panel shows the gain of DTGC applied to the received sinusoidal signals
in decibel scale
95
compressed envelope information of signals without DTGC was obtained as shown
in the left panel of Figure 5-6. To see the effect of DTGC on the image, the DTGC
gains along time shown in the middle panel of the figure were applied to the output
of the DC canceller. The resultant image in the right panel of the figure shows that
Figure 5-7: Effect of DTGC on the A-line samples after the DC canceller shown
in Figure 5-4. The middle panel is the DTGC gains applied to the processing.
96
the intensity of envelope information is gradually increased along with the DTGC
gains.
Figure 5-7 is the resultant A-line samples from DTGC of the samples obtained
by the DC canceller shown in Figure 5-4. The middle panel of the figure is the
DTGC gains applied to the processing. The result illustrates that the digital time gain
compensator increases not only the level of meaningful signals but also noise level.
This phenomenon explains the fact that the role of DTGC is for the overcome of the
mismatch problem of dynamic ranges between echo signals received by a transducer
and system capability, not for the improvement of signal-to-noise ratio.
5.2.3 PCI Bus Controller
To deal with echo signals coming from the scanner at a rate of more than 100
frames per second, the back-end processing system must be completed within less
than 10 ms. As discussed in Chapter 3 and 4, the proposed designs are capable of
supporting the time requirement. In addition to producing scan converted images,
fast data transfer to PC is needed to display and to store the images on the fly. The
required data transfer rate is about 27 Mbytes per second for transferring 100 images
per second in which each image is composed of 256,144 pixels (512 by 512 image
size). In order to achieve the wide bandwidth of data transfer, the PCI bus controller
in Figure 5-3 employs the master mode operation of PCI bus with direct memory
97
access (DMA) method. By doing so, the DSC board can send image data to random
access memory (RAM) in PC without the minimal interruption of CPU.
Figure 5-4 describes the block diagram of the PCI bus controller responsible
for the interface between PCI bus and DSC board. The DMA registers and DSC
registers in the figure are memory-mapped registers so that the user interface module
can directly read and write their values via the PCI bus. The DSC control signal
generator produces control signals related to writing LUTs, reading display memory
Figure 5-8: Block diagram of PCI bus controller employing master mode PCI
operation with direct memory access (DMA) method. The dashed arrows
represent control signals and the solid arrows represent data flows.
98
banks, and the reset of digital logics in the DSC board. The DMA control logic
changes the DMA register values associated with the transactions of master mode
operation. A first-in-first-out (FIFO) buffer is required to serve as a buffer space for
data transfer between PCI bus and DSC board because their operating clock rates,
i.e., data rates are different. The master control logic is involved in requesting the
ownership of PCI bus to PCI arbiter and the generation of control signals to the
DMA control logic and the DSC-control-signal generator.
Once the display memory bank named as DM bank zero is ready to send one
frame of image data to the user interface module, the display-memory-control logic
in DSC board sets the DM bank 0 register to one. In the case that the bank number is
one, the DM bank 1 register becomes one. The user interface module checks the
status of the display memory banks by reading the values of these registers in order
to determine whether to request the DSC board to send out the image data. For the
sake of burst data transfer in the master mode, the user interface module firstly writes
values of one into two bits representing a write command and a DMA enable request
in the control-and-status register. If the DMA enable bit becomes one, the master
control logic can request the ownership of PCI bus from PCI arbiter. The second step
is that the user interface module sets the local address register and the byte counter
register with a display-memory-start address and a total number of bytes to be
transferred. The master control logic requests the DSC-control-signal generator to
produce a display-memory-bank-read-enable signal and read addresses. The display-
memory-start address determines a target-display-memory bank: 0x00000 for the
99
bank number zero and 0x40000 for the bank number one. The value of the byte
counter is decreased by eight after every data transfer on PCI bus because eight bytes
data are transferred in one transaction. The final step is that the user interface module
sets the PCI-bus-address register with the PCI-bus-start address corresponding to the
RAM address in PC. This register value is increased by eight after every data transfer
on the PCI bus. Once the PCI-bus-address register is filled, the master control logic
starts PCI-master-write operation to transfer pixel data into RAM in PC. The PCI-
master-read operation that fetches the entries of LUTs from RAM in the PC follows
similar steps in the writing operation; the difference is writing an address identifying
a target LUT to the local address register, and setting a read command bit in the
control-and-status register to one instead of the write command bit.
Theoretical maximum data transfer rate of the PCI bus on the master mode
operation with DMA is 266 Mbytes per second, which completely satisfies the
requirement for data transfer speed. However, its real speed will be much less than
the theoretical speed depending on the number of PCI devices connected to the PC
which determines PCI bus congestion. Nevertheless, more than 27 Mbytes per
second is achievable by efficient programming of PCI driver and controlling a video
card.
5.2.4 User Interface Module
100
(a)
(b)
Figure 5-9: Graphic user interface (GUI). When a user clicks either DSC (a) or
DTGC (b) Parameter Setting menu bar, a dialog box pops up so as to input the
desired parameters.
101
The user interface module consists of a PCI interface involving PCI device
driver, a graphic card controller with OpenGL API, and a graphic user interface
(GUI) programmed by using Microsoft Foundation Class (MFC). The user interface
module has three main menu bars: one is the control menu related to resetting the
DSC board and starting image display on a monitor, another is the DSC parameter
Figure 5-10: Flow chart of the user interface module. Gray colored boxes
involves a PCI device driver and a bold outlined box represents a function
implemented by OpenGL API.
102
setting menu in which the characteristics of scanner and image configuration are
input, the other is the DTGC parameter setting menu as shown in Figure 5-9. Figure
5-6 shows a flow chart of the user interface module. In the figure, gray boxes
represent functions involving PCI device driver and a bold outlined box represents a
function implemented by OpenGL API.
5.3 Experimental Results
The performance of the back-end processing system developed in this work
was evaluated with respect to processing speed and image quality. All experiments,
presented here, used two 40-MHz light-weight (less than 0.28 g) single element
transducers (Cannata et al., 2003). In Table 5-1, the parameters of the transducers are
summarized. And the left panel in Figure 5-11 shows a photograph of the single
Table 5-1: Parameters of the single element transducers used in the experiments
Transducer
Types
Center
Frequency
-6 dB
Bandwidth
Focal
Depth
F-number
Insertion
Loss
A 40 MHz 22.8-56 MHz 6.2 mm 2.1 22.9 dB
B 40 MHz 26.15-54 MHz 8 mm 2.5 19.9 dB
103
element transducers; the upper one is the type B and the lower one is the type A. And
the upper plots of the right panel in Figure 5-11 show the pulse-echo response and
frequency spectrum of type A, and the lower plots is these of type B.
Figure 5-12 shows the mechanical sector scanner (a) and the back-end
processing system (b) described in Section 5-1 and 5-2, respectively. For the
experiments, a MATEC DEX-3 diode expander, a MATEC DL-1 diode limiter, and
a 35-dB preamplifier (AU-1466-BLC, MITEQ, Hauppauge, NY) with a BPF (BIF-
40, Mini-Circuits, Brooklyn, NY) were used. And the transducers were excited by
Figure 5-11: Pulse-echo responses and frequency spectrums of the 40-MHz
single element transducers used in the experiments. The left panel shows a
photograph of the transducers; the upper one is the type B and the lower one is
the type A. The upper plots of the right panel show the pulse-echo response and
frequency spectrum of type A, and the lower plots is these of type B.
104
using a commercial high voltage pulser (5900PR, Panametrics, Inc., Waltham, MA).
(a)
(b)
Figure 5-12: Experiment arrangement: mechanical sector scanner (a) and the
back-end processing system developed (b).
105
5.3.1 Processing Speed
Since a very fast scanning system allowing for the evaluation of the maximum
processing speed of the back-end processing system developed is presently not
available, it was performed by using four-cycle sinusoidal burst signals with 25-MHz
center frequency generated by a function generator (33250A, Agilent Technologies
Inc., Palo Alto, CA). Scan conversion with the maximum frame rate was performed
under the condition where the number of scanlines was 200 and total view angle was
15 degrees. Scan converted images were sent to the host processing block and stored
in the hard disk of PC with a time stamp. The time stamp recorded in a file showed
Figure 5-13: Image obtained by the scan conversion with four-cycle 25-MHz
sinusoidal burst signals created by a function generator.
106
that the maximum frame rate was 400 frames per second, where the pulse repetition
frequency (PRF) handled by the scan converter was 80 KHz. The frame rate is the
maximum obtainable value with 100-MHz operation clock and 256 by 256 image
size. On the other hand, the display rate of the images was 95 images per second due
to the limitation of a monitor’s capability. This display rate was evaluated by an
experiment in which PRF was increased while displaying one out of two images. The
maximum PRF without missing an image was 38.5 KHz corresponding to about 190
images per second (
3
38.5 10 200 ×÷ ), thus a half of 190 images per second were
regarded as the maximum display rate. Figure 5-13 shows a resultant image from the
scan conversion with four-cycle sinusoidal burst signals.
In order to examine the temporal resolution of the system, the motion of a stir
bar rotating in a water-filled container by a magnetic hot plate stirrer (PC-420,
Corning Inc., NY) was acquired. The stir bar was rotated at the rate of 3.33 half turns
per second. This means that we can see a halfly rotated stir bar every 300 ms (1/3.33).
Figure 5-14 shows the images of the rotating stir bar with their time stamps.
According to the time stamps, the time to obtain an image is between 15 ms and 16
ms except for the third and fourth images resulting from lowering the swing speed of
a transducer due to interference of the stir bar. The time corresponds to the scanning
rate of 64 frames per second, which is equal to that of the mechanical sector scanner.
In addition, it is seen in Figure 5-14 that the stir bar with hexagonal shape in cross
section was rotated a little more than 180 degrees after 312 ms that well matched
with the expectation value 300 ms if the experimental error caused by mutual
107
interferences between the rotating stir ring bar and the swing transducer is taken into
account.
Figure 5-14: Images of a rotating stir bar with their time stamps. Because the stir
bar has a hexagonal shape in cross section, the top and side parts of the bar are
shown in the images; the flat line extending in horizontal direction is the top part
of the bar.
108
5.3.2 Image Quality
The spatial resolution and the accuracy of the back-end processing system were
evaluated by wire phantom testing with the type B transducer. Figure 5-15 shows a
photograph and schematic of a wire phantom used for this experiment, which is
consisting of five 20 m μ diameter tungsten wires (California Fine Wire Co., CA)
separated by distance intervals along vertical and horizontal directions of 1.5 mm and
0.65 mm, respectively. In order to form a wire phantom image, the back-end
processing system worked under the condition where the total scanlines constituting
Figure 5-15: Photograph (left side) and schematic (right side) of a wire phantom
consisting of five 20 m μ diameter tungsten wires of which distance intervals
along vertical and horizontal direction are 1.5 mm and 0.65 mm, respectively.
109
a frame were 108, the scanning angle was 12.8 degrees, and the dynamic range of
logarithmic compression was 60 dB. The resultant wire phantom image is shown in
Figure 5-16.
The scan conversion was performed with 2048 samples so that imaging depth
was 7.88 mm by Equation (5-1).
3
6
2048 1540 10
Imaging Depth
2 200 10
mm
××
=
× ×
(5−1)
Since the scan conversion started from 4 mm depth, the maximum image depth is
11.88 mm, so that the third wire image in the vicinity of the focal depth of the
Figure 5-16: Wire phantom image obtained using the type B transducer.
110
transducer, 8 mm, has the best spatial resolution: the -6dB axial and lateral resolution
of 48 m μ and 103 m μ , respectively.
In order to evaluate the accuracy of the system, echo signals (or RF data) were
acquired without any back-end processing under the same condition as the previous
experiment. The envelope detection of the acquired RF (radio-frequency) data was
performed in a computer and the maximum value of the extracted envelope was
found, which will be located at a similar position to the peak value of the third wire
image. The scanline containing the maximum envelope was used for evaluating the
accuracy of the system’s axial resolution. And the samples in each scanline, which
were acquired at the same time as the sample with the maximum envelope, were
used for evaluating the accuracy of the system’s lateral resolution. The -6 dB axial
and lateral resolutions computed from RF data are, respectively, 45 m μ and 110
m μ that are similar to the spatial resolution of the system developed. This means
that the system is capable of providing very accurate results because of its negligible
signal processing error.
Figure 5-17 illustrates the -6 dB axial and lateral beam profiles of the third wire
image obtained from the system (solid line) and RF data (dashed line). This figure
shows that the main lobes of the beam profiles obtained from the two methods have
similar shapes but their side lobes are different. This is so because the locations of
RF samples and pixels are not exactly equal; the RF samples were acquired in a polar
coordinate but pixels are located in a Cartesian coordinate. However, the different
location problem has little effect on the evaluation of -6dB spatial resolution.
111
(a)
(b)
Figure 5-17: The beam profiles of the third wire image shown in Figure 5-16; the
-6 dB axial (a) and lateral (b) resolution obtained from the system (solid line) are
48 m μ and 103 m μ , respectively. On the other hand, these from RF data (dashed
line) are 45 m μ and 110 m μ , respectively.
112
As mentioned in Chapter 1, ophthalmic imaging is one of high frequency
ultrasound imaging applications. Transducers with frequency range of 40 MHz to 50
MHz are suitable for the diagnosis of diseases of the anterior segment of the eye such
as tumors growing within the iris and glaucoma evaluated with the anterior chamber
angle. In vitro imaging of a pig eye verified the capability of the system to diagnose
the diseases of the anterior segment of the eye. Figure A-1 shows the anatomy of the
human eye as a reference.
In this experiment, the type A transducer was used, and the maximum swing
angle of the transducer and the number of scanlines were 12.8 degrees and 108,
Figure 5-18: Image of the anterior segment of a pig eye obtained in vitro
113
respectively. The scan conversion started from 1.3 mm depth and LOG compression
with a 60 dB dynamic range was performed. Figure 5-18 is a pig eye image showing
the cornea, the iris, and the lens. In the figure, we can clearly see the cornea and the
boundary between the iris and the lens which is the starting point of the pupil. Since
tumors within the iris is cyst type and changes the thickness of the iris, with
resolution provided by the system we may diagnose tumors in the iris and evaluate
the depth of an iris tumor.
Figure 5-19 is a pig eye image illustrating the sclera commonly known as the
Figure 5-19: Pig eye image illustrating the sclera commonly known as the white
of the eye, cornea join forming anterior chamber angle, zonular fibers located
behind the iris, and the ciliary body
114
white of the eye, cornea join forming anterior chamber angle, zonular fibers located
behind the iris, and the ciliary body. In this figure, we can see the cornea joint in
spite of a relatively high frequency-dependent attenuation of the ciliary body and the
sclera right above the join (Ye et al., 1992). Because glaucoma is related to the
increase of intraocular pressure that changes the anterior chamber angle, the system
may offer the diagnosis of glaucoma from the assessment of the angle.
In vivo experiment of the mouse heart was performed under a protocol
approved by the Institutional Animal Care and Use Committee (IACUC) at the
University of Southern California. And this experiment was carried out with the
same condition as the in vitro experiment except for the number of scanlines of 56.
For the experiment, a two week old mouse was anesthetized with pentobarbital
Figure 5-20: Photograph of the setup for in vivo mouse heart imaging.
115
sodium diluted in saline to 4 mg ml via the intraperitoneal injection of a dose of 10
lg μ body weight, and it was cleaned with a chemical hair remover. The bottom of
water-filled container was in contact with the mouse with ultrasound gel as a
coupling medium as shown in Figure 5-20.
Figure 5-21 shows still images of moving the mouse heart acquired at the rate
of 67 images per second. In the first two frame acquired at t = 0 ms and t = 15 ms, we
can see the left ventricle (LV), the left atrium (LA), and the pulmonary artery (PA).
Because the mitral valve (MV) closes, however, it is not shown in the frames. From
the third frame acquired at t = 30 ms, the MV starts to open, so that it is visible. This
experimental result indicates that the back-end processing system developed in the
work is capable of adequately providing the information about the cardiac activity of
the mouse.
5.4 Conclusion
In the Chapter, a high speed back-end processing system for high frequency
ultrasound imaging has been described. The system developed is capable of handling
up to 400 images per second at 100 MHz system clock frequency while displaying
up to 95 images per second on a monitor. The performance in terms of processing
speed and image quality of the system has been verified by the phantom, in vitro, and
in vivo experiments.
116
Figure 5-21: Still images of moving the mouse heart acquired at the rate of 67
images per second. LA: left atrium, LV: left ventricle, MV: mitral valve, PA:
pulmonary artery.
117
CHAPTER 6
SUMMARY AND FUTURE WORK
6.1 Summary
High frequency ultrasound is capable of providing fine spatial resolution on the
order of several tens of micrometers and fine temporal resolution of more than 100
frames per second, which are among the best in medical imaging modalities.
Therefore, high frequency ultrasound is especially useful for the eye, skin,
intravascular, and small animals imaging that are applications requiring a very high
resolution within relatively small imaging area. Especially, the capabilities of high
frequency ultrasound are applicable to the cardiac imaging of the mouse where the
heart rate is 5-10 beats per second. In order to adequately capture the cardiac activity
of the mouse, two key system elements are required: high-speed acquisition of echo
signals (front-end system) and high-speed signal processing functions to extract
clinically useful information from the acquired echo signals and to display the
information on a monitor in real time (back-end system). High-speed data acquisition
can be achieved by either electronic scanning with high frequency linear array
transducers or mechanical scanning with single element or annular array transducers.
However, it is still challenging to develop high-speed signal processing functions to
support high frame rate imaging in real time. This is so because they must have the
118
capability of a very fast computational speed and wide bandwidth of data transfer
between each functional block.
The goal of this research was to develop a back-end processing system capable
of supporting high frequency ultrasound B-mode imaging with fine spatial and
temporal resolutions, in which an envelope detector, a logarithmic compressor, and a
digital scan converter are involved. In order to achieve the goal, a novel envelope
detector containing a logarithmic compression function for high frame rate high
frequency ultrasound imaging has been proposed. The new LUT strategy employed
by the proposed envelope detector makes it possible to achieve very fast operating
speed as well as good accuracy. The performance of the proposed design was
examined and the results have shown that the proposed design is suitable for
envelope detection in a high frame rate high frequency ultrasound imaging system in
terms of operating speed and accuracy.
In addition, a high frame rate digital scan converter (DSC) mapping acquired
echo samples into monitor pixels has been developed and described. In order to
achieve the desired processing speed, the developed system employed the linear
interpolation algorithm in which two nearest samples to each object image pixel are
selected and an angular interpolation is performed. Therefore, memory access time to
fetch samples was one clock cycle. Coordinate transformation of a given pixel
location was realized by a look-up table method, thus spending one clock cycle. In
the system developed, the main time bottleneck was the pixel address generator
responsible for providing assigned pixel addresses to the coordinate transformer,
119
which was 3 clock cycles.
The processing functional blocks were assembled and implemented in a single
field programmable gate array (FPGA). For fast data transfer, this system adopted a
64-bit 33 MHz PCI bus on a master operation mode with direct memory access
(DMA). By experiments, it was shown that the system is capable of acquiring up to
400 images per second and its image display rate is 95 images per second due to the
limitation of a monitor’s capability although all scan converted images can be stored
in the hard disk of a personal computer. The capability of the system to support high
frequency ultrasound front-end system was examined by in vitro and in vivo
experiment on the pig eye and the mouse heart.
6.2 Future Work
The quality of ultrasound B-mode images can be improved by adopting such
imaging techniques capable of offering good signal-to-noise ratio (SNR) and spatial
resolution as synthetic aperture focusing, coded excitation, and image compounding
methods. Among these methods, the coded excitation and image compounding are
applicable to high-frequency ultrasound imaging with the mechanical sector
scanning.
120
6.2.1 Coded Excitation for Improving SNR
In general, ultrasound images suffer from frequency-dependent attenuation
causing low SNR to echo signals from far field. This phenomenon is much serious in
high frequency ultrasound imaging with small aperture-sized transducers. The
simplest way to improve SNR in the situation is to increase input power to excite
transducers. However, this method is not an ideal solution due to the regulatory
limitation of peak pressure to prevent potential bioeffects. In order to overcome the
limitation, the coded excitation technique (O’Donnell, 1992) can be used in which
code sequences are transmitted through a transducer and the received code sequences
are compressed with either a matched or a mismatched filter as a decoder; the code
sequences include phase codes like Barker and Golay codes modulated by a carrier
frequency and frequency codes like chirp code generated by linear frequency
modulation (FM). According to O’Donnell (1992), this technique is capable of
providing the SNR improvement of up to 20 dB.
For high-speed high-frequency ultrasound imaging, the use of the Golay code
is not suitable because it requires at least two transmissions for a scanline, thus
degrading temporal resolution. From the same reason, therefore, the performance of
the Golay code is susceptible to tissue motion like heart (Chiao and Hao, 2005).
Although the chirp code is capable of providing good range resolution and sidelobe
suppression as well as the full use of the bandwidth of a transducer allowing good
SNR improvement (Misaridis and Jensen, 2005), the adoption of this code requires a
121
complicated and high-cost imaging system that involves a multilevel transmitter and
a multilevel decoder using matched or mismatched filters. Especially, the
implementation of the transmitter and decoder in high frequency ultrasound imaging
systems is much more difficult because of high-speed operating clock rate. As a
result, the Barker code can be a good candidate for high frequency ultrasound
imaging in order to improve depth of penetration or SNR due to the relatively simple
implementation of a transmitter and a decoder. In order to use the Barker code for
high frequency ultrasound imaging, the implementation of a biphase modulator
operating at more than 50 MHz and the optimal design of a decoder to suppress a
range sidelobe level to at least -60 dB are needed.
6.2.2 Frequency Compounding by Using Dual Element Transducers
Ultrasound images usually contain speckle pattern attributed to interaction
between ultrasound and scatterers in tissues, i.e., the constructive and destructive
interference effects. This speckle pattern is undesirable because it degrades contrast
and SNR of ultrasound images if it is regarded as noise. The speckle pattern can be
suppressed by either frequency compounding (Magnin et al., 1982; Cincotti et al.,
2001) or spatial compounding (Burckhardt, 1978; Trahey et al., 1986) at the expense
of exasperating spatial resolution; these involve the average process of images
obtained under different scanning conditions for the same object after envelope
122
detection. By applying these methods to imaging, SNR can be improved by a factor
of N , where N is a number of images with uncorrelated speckle pattern, which are
used for averaging (Burckhardt, 1978). If two images are averaged, for example, the
factor of the SNR improvement will be 1.414. Note that if the speckle patterns in the
two images are correlated, we will achieve much less SNR improvement than the
factor.
In the frequency compounding method, a fixed bandwidth of original RF
signals obtained by one frame scanning is divided into two to four frequency
subbands. RF signals obtained by the bandwidth division are used to form images;
RF signal of one frequency subband forms an image. A compound image is
produced by adding or averaging the images either with or without weighting factors.
Speckle correlation between the images is determined by the center frequency
difference, f Δ , and -6dB bandwidth,
6dB
BW
−
, of the subband RF signals (Trahey
and Allison et al., 1986), and the relationship can be expressed as:
1
2
2
6
f
BW
dB
e ρ
−
⎛⎞ Δ
⋅
⎜⎟
− ⎝⎠
= (6−1)
where ρ is the speckle correlation coefficient. As seen in this equation, the -6dB
bandwidth should be narrow in order to obtain low enough speckle correlation
between the images formed by frequency division of a fixed-bandwidth of original
RF signals. This means that the axial resolution of compound images can be
seriously degraded. For this reason, Trahey et al. (1986) pointed out that spatial
123
compounding performed by division of available aperture into overlapping
subapertures is favorable for the improvement of image quality. This is so because
speckle reduction rate by the spatial compounding with a given loss of lateral
resolution is much larger than that by frequency compounding with the same loss of
axial resolution. From the same reason, therefore, the spatial compounding is also
favorable for high frequency ultrasound imaging rather than the frequency
compounding. However, the spatial compounding is not suitable for the high
frequency ultrasound imaging with a single element transducer when it comes to a
high-speed acquisition of echo signals. This is so because the spatial compounding
method involves several scanning steps to form an image, thus degrading temporal
resolution as well as lateral resolution.
A possible way to take full advantage of frequency compounding is the use of a
dual element transducer developed for high frequency ultrasound harmonic imaging
(Kim et al., 2006). The transducer consists of two annular elements with different
center frequencies; the outer annulus is for transmitting 18-MHz signals and the
inner annulus is for receiving 35-MHz echoes that are the second harmonic signals of
the transmitted signals. Exciting the two elements at the same time instead of only
the outer annulus, a transmitter generates different shapes of signals from each
annulus as shown in Figure 6-1; the outer and the inner annuli fire 18-MHz and 28-
MHz center frequency signals, respectively. These signals travel along different
paths and come back to each annular element after interaction with tissue
components. Because of the different center frequencies, traveling paths, and
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properties of the transducer elements, echo signals received by the two elements may
contain different speckle patterns. This means that each element may receive echo
signals with low enough speckle correlation even over the same frequency range.
This idea is confirmed by Figure 6-2 showing echo signals from the posterior
segment of a pig eye, which were received by the outer (top panel) and the inner
Figure 6-1: Transmit signals and their frequency spectrums generated from a dual
element transducer.
125
(bottom panel) annuli. As seen in the figure, the two echo signals received from 40.2
s μ , i.e., after reflection from the main layer of the posterior segment have different
shapes and their correlation coefficient is less than 0.2 with which the two echo
signals can be regarded as uncorrelated signals. With minimal degradation of axial
resolution, therefore, we may obtain a frequency compounding image by averaging
two uncorrelated images formed with echo signals received by each annulus. In order
to do so, a two-channel receiving module including DC cancellers, DTGCs, envelope
detectors, and an image blender with variable weighting function for each channel
should be implemented.
Figure 6-2: Echo signals from the posterior segment of a pig eye, which were
received by the outer (top panel) and the inner (bottom panel) annuli.
126
BIBLIOGRAPHY
K. H. Abed and R. E. Siferd, “CMOS VLSI implementation of a low-power
logarithmic converter,” IEEE Trans. Computers, vol. 52, no. 11, pp. 1421-1433,
2003.
R. E. Baddour, M. D. Sherar, J. W. Hunt, G. J. Czarnota, and M. C. Kolios, “High-
frequency ultrasound scattering from microspheres and single cells,” J. Acoust. Soc.
Am., vol. 117, no. 2, pp. 934-943, 2005.
A. P. Berkhoff, H. J. Huisman, J. M. Thijssen, E. M. G. P. Jacobs, and R. J. F.
Homan, “Fast scan conversion algorithms for displaying ultrasound sector images,”
Ultrason. Imag., vol. 16, pp. 87-108, 1994.
J. A. Brown and G. R. Lockwood, “A digital beamformer for high-frequency annular
arrays,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 52, no. 8, pp. 1262-
1269, 2005.
C. B. Burckhardt, “Speckle in ultrasound B-mode scans,” IEEE Trans. Sonics
Ultrason., vol. SU-25, no. 1, pp. 1-6, 1978.
J. M. Cannata, T. A. Ritter, W. –H. Chen, R. H. Silverman, and K. K. Shung,
“Design of efficient, broadband single-element (20-80 MHz) ultrasonic transducers
for medical imaging applications,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr.,
vol. 50, no. 11, pp. 1548-1557, 2003.
J. M. Cannata, J. A. Williams, Q. Zhou, T. A. Ritter, K. K. Shung, “Development of
a 35-MHz piezo-composite ultrasound array for medical imaging,” IEEE Trans.
Ultrason., Ferroelect., Freq. Contr., vol. 53, no. 1, pp. 224-236, 2006.
J. H. Chang, J. T. Yen, and K. K. Shung, “A novel envelope detector for high-frame
rate, high-frequency ultrasound imaging,” IEEE Trans. Ultrason., Ferroelect., Freq.
Contr., vol. 54, no. 9, pp. 1792-1801, 2007.
127
E. Chérin, R. Williams, A. Needles, G. Liu, C. White, A. S. Brown, Y. –Q. Zhou,
and F. S. Foster, “Ultrahigh frame rate retrospective ultrasound microimaging and
blood flow visualization in mice in vivo,” Ultrasound in Med. & Biol., vol. 32, no. 5,
pp. 683-691, 2006.
R. Y. Chiao, X. Hao, “Coded excitation for diagnostic ultrasound: a system
developer’s perspective,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 52,
no. 2, pp. 160-170, 2005.
G. Cincotti, G. Loi, and M. Pappalardo, “Frequency decomposition and
compounding of ultrasound medical images with wavelet packets,” IEEE Trans. Med.
Imag., vol. 20, no. 8, pp. 764-771, 2001.
D. J. Coleman, R. H. Silverman, A. Chabi, M. J. Rondeau, K. K. Shung, J. Cannata,
H. Lincoff, “High-resolution ultrasonic imaging of the posterior segment,”
Ophthalmology, vol. 111, no. 7, pp. 1344-1351, 2004.
F. S. Foster, C. J. Pavlin, G. R. Lockwood, L. K. Ryan, K. A. Harasiewicz, L Berube,
and A. M. Rauth, “Principles and applications of ultrasound backscatter
microscopy,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 40, no. 5, pp.
608-616, 1993.
F. S. Foster, C. J. Pavlin, K. A. Harasiewicz, D. A. Christopher, and D. H. Turnbull,
“Advances in ultrasound biomicroscopy,” Ultrasound in Med. & Biol., vol. 26, no. 1,
pp. 1-27, 2000.
F. S. Foster, G. Liu, J. Mehi, B. S. Starkoski, L. Adamson, Y. Zhou, K. A.
Harasiecwicz, and L. Zan, “High frequency ultrasound imaging: from man to
mouse,” in Proc. IEEE Ultrason. Symp., 2000, pp. 1633-1638.
F. S. Foster, M. Y. Zhang, Y. Q. Zhou, G. Liu, J. Mehi, E. Cherin, K. A. Harasiewicz,
B. G. Starkoski, L. Zan, D. A. Knapik, and S. L. Adamson, “A new ultrasound
instrument for in vivo microimaging of mice,” Ultrasound in Med. & Biol., vol. 28,
no. 9, pp. 1165-1172, 2002.
128
S. G. Foster and M. H. Wheeler, “Time gain compensation implementation,” United
States Patent, #5,501,221, 1996.
C. –H. Hu, X. –C. Xu, J. M. Cannata, J. T. Yen, and K. K. Shung, “Development of
a real-time, high-frequency ultrasound digital beamformer for high-frequency linear
array transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 53, no. 2,
pp. 317-323, 2006.
J. S. Hwang and T. K. Song, “A study of the display pixel-based focusing method in
ultrasound imaging,” Ultrason. Imag., vol. 22, pp. 1-18, 2001.
J. A. Jensen and N. B. Svendsen, “Calculating of pressure fields from arbitrarily
shaped, apodized, and excited ultrasound transducers,” IEEE Trans. Ultrason.,
Ferroelect., Freq. Contr., vol. 39, pp. 262-267, 1992.
J. A. Jensen, “Field: A program for simulating ultrasound system,” 10
th
Nordic-
Baltic conference on Biomedical Imaging, vol. 4, pp. 351-353, 1996.
H. H. Kim, J. M. Cannata, R. H. Silverman, R. Liu, S. Babar, L. Sun, and K. K.
Shung, “Dual element transducers for high frequency harmonic imaging,” in Proc.
IEEE Ultrason. Symp., 2006, pp. 2325-2328.
I. Koll ár, R. Pintelon, J. Schoukens, “Optimal FIR and IIR Hilbert transformer
design via LS and Minimax fitting,” IEEE Trans. Instrum. Meas., vol. 39, no. 6, pp.
847-852, 1990.
I. Koren, Computer Arithmetic Algorithms. 2
nd
ed., A. K. Peters, Ltd., Natick, MA,
2002.
T. Kurokawa, J. A. Payne, and S. C. Lee, “Error analysis of recursive digital filters
implemented with logarithmic number system,” IEEE Trans. Acoust., Speech, Signal
Processing, ASSP-28, no. 6, pp. 706-715, 1980.
129
T. I. Laasko, V. Valimaki, M. Karjalainen, and U. K. Laine, “Splitting the unit
delay,” IEEE Signal Processing Mag., vol. 13, pp. 30-60, 1996.
H. G. Larsen and S. C. Leavitt, “An image display algorithm for use in real time
sector scanners with digital scan converters,” in Proc. IEEE Ultrason. Symp., 1980,
pp. 763-765.
S. C. Leavitt, H. G. Larsen, and B. F. Hunt, “Scan Converter System,” United States
Patent, #4,471,449, 1984.
M. H. Lee, J. H Kim, and S. B. Park, “Analysis of a scan conversion algorithm for a
real time sector scanner,” IEEE Trans. Med. Imag., vol. MI-5, no. 2, pp. 96-105,
1986.
H. –D. Liang and M. J. K. Blomley, “The role of ultrasound in molecular imaging,”
Br. J. Radiol., vol. 76, pp. S140-S150, 2003.
J. –H. Liu, G. –S. Jeng, T. –K. Wu, and P. –C. Li, “ECG triggering and gating for
ultrasonic small animal imaging,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr.,
vol. 53, no. 9, pp. 1590-1596, 2006.
H. –Y. Lo and Y. Aoki, “Generation of a precise binary logarithm with difference
grouping programmable logic array,” IEEE Trans. Computers, C-34, no. 8, pp. 681-
691, 1985.
G. R. Lockwood, L. K. Ryan, A. I. Gotlieb, E. Lonn, J. W. Hunt, P. Lui, and F. S.
Foster, “In vitro high resolution intravascular imaging in muscular and elastic
arteries,” J. Amer. Coll. Cardiol., vol. 20, pp. 153-160, 1992.
G. R. Lockwood, D. H. Turnbull, D. A. Christopher, and F. S. Foster, “Beyond 30
MHz: applications of high frequency ultrasound imaging,” IEEE Eng. Med. Biol.
Mag., vol. 15, pp. 60-71, 1996.
P. A. Magnin, O. T. von Ramm, F. L. Thurstone, “Frequency compounding for
130
speckle contrast reduction in phased array images,” Ultrason. Imag., vol. 4, pp. 267-
281, 1982.
T. Misaridis and J. A. Jensen, “Use of modulated excitation signals in medical
ultrasound. Part I: basic concepts and expected benefits,” IEEE Trans. Ultrason.,
Ferroelect., Freq. Contr., vol. 52, no. 2, pp. 177-191, 2005.
P. Montuschi, M. Mezzalama, “Survey of square rooting algorithms,” IEE Proc., vol.
137, no. 1, pp. 31-40, 1990.
R. A. Mucci, “A comparison of efficient beamforming algorithms,” IEEE Trans.
Acoust., Speech, Signal Processing, ASSP-32, no. 3, pp. 428-557, 1984.
H. J. Nitzpon, J. C. Rajaonah, C. B. Burckhardt, B. Dousse, and J. J. Meister, “A
new pulsed wave Doppler ultrasound system to measure blood velocities beyond the
Nyquist limit,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 42, no. 2, pp.
265-279, 1995.
M. O’Donnell, W. E. Engeler, J. T. Pedicone, A. M. Itani, S. E. Noujaim, R. J.
Dunki-Jacobs, W. M. Leue, C. L. Chalek, L. S. Smith, J. E. Piel, R. L. Harris, K. B.
Welles, and W. L. Hinrichs, “Real-time phased array imaging using digital beam
forming and autonomous channel control,” in Proc. IEEE Ultrason. Symp., 1990, pp.
1499-1502.
M. O’Donnell, “Coded excitation system for improving the penetration of real-time
phased-array imaging systems,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr.,
vol. 39, no. 3, pp. 341-351, 1992.
J. Ophir and N. F. Maklad, “Digital scan converters in diagnostic ultrasound
imaging,” Proc. IEEE, vol. 67, no. 4, pp. 654-664, 1979.
A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing,
2
nd
ed. Upper Saddle River, NJ: Prentice-Hall, 1998, chap. 11.
131
C. Passmann and H. Ermert, “A 100-MHz ultrasound imaging system for
dermatologic and ophthalmologic diagnostics,” IEEE Trans. Ultrason., Ferroelect.,
Freq. Contr., vol. 43, no. 4, pp. 545-552, 1996.
R. N. Phelps, H. Wang, Z. B. Banjanim, and P. T. Kuhn, “System and method for re-
orderable nonlinear echo processing,” United States Patent, #6,689,060, 2004.
J. Prado and R. Alcantara, A fast square-rooting algorithm using a digital signal
processor,” Proc. IEEE, vol. 75, no. 2, pp. 262-264, 1987.
S. D. Pye, S. R. Wild, and W. N. McDicken, “Adaptive time gain compensation for
ultrasonic imaging,” Ultrasound in Med. & Biol., vol. 18, no. 2, pp. 205-212, 1992.
O. T. V. Ramm and S. W. Smith, “Beam steering with linear arrays,” IEEE Trans.
Biomed. Eng., vol. BME-30, no. 8, pp. 438-452, 1983.
T. L. Rhyne, “Characterizing ultrasonic transducers using radiation efficiency and
reception noise figure,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 45, no.
3, pp. 559-566, 1998.
W. D. Richard, “A new time-gain correction method for standard B-mode ultrasound
imaging,” IEEE Trans. Med. Imag., vol. 8, no. 3, pp. 283-285, 1989.
W. D. Richard and R. M. Arthur, “Real-time ultrasonic scan conversion via linear
interpolation of oversampled vectors,” Ultrason. Imag., vol. 16, pp. 109-123, 1994.
T. A. Ritter, T. R. Shrout, R. Tutwiler, and K. K. Shung, “A 30-MHz piezo-
composite ultrasound array for medical imaging applications,” IEEE Trans.
Ultrason., Ferroelect., Freq. Contr., vol. 49, no. 2, pp. 217-230, 2002.
D. E. Robinson and P. C. Knight, “Interpolation scan conversion in pulse-echo
ultrasound,” Ultrason. Imag., vol. 4, pp. 297-310, 1982.
132
M. Schlaikjer, J. P. Bagge, O. M. Sorensen, and J. A. Jensen, “Trade off study on
different envelope detectors for B-mode imaging,” in Proc. IEEE Ultrason. Symp.,
2003, pp. 1938-1941.
M. –H. Schmid-Wendtner and W. Burgdorf, “Ultrasound scanning in dermatology,”
Arch. Dermatol., vol. 141, pp. 217-224, 2005.
K. K. Shung, Diagnostic ultrasound: imaging and blood flow measurements, Boca
Raton, FL: Talyer and Francis, 2005.
S. Sikdar, R. Managuli, T. Mitake, T. Hayashi, and Y. Kim, “Programmable
ultrasound scan conversion on a Mediaprocessor-based system,” in Proc. SPIE Med.
Imag., vol. 4319, pp. 699-711, 2001.
S. Sikdar, R. Managuli, L. Gong, V. Shamdasani, T. Mitake, T. Hayashi, and Y. Kim,
“A single mediaprocessor-based programmable ultrasound system,” IEEE Trans.
Inform. Technol. Biomed., vol. 7, no. 1, pp. 64-70, 2003.
T. K. Song and S. B. Park, “A new digital phased array system for dynamic focusing
and steering with reduced sampling rate,” Ultrason. Imag., vol. 12, pp. 1-16, 1990.
L. Sun, W. D. Richard, J. M. Cannata, C. C. Feng, J. A. Johnson, J. T. Yen, and K. K.
Shung, “A high-frame rate high-frequency ultrasonic system for cardiac imaging in
mice,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 54, no. 8, pp. 1648-
1655, 2007.
T. L. Szabo, Diagnostic ultrasound imaging: inside out, San Diego, CA: Elsevier
Academic Press, 2004.
F. J. Taylor, R. Gill, J. Joseph, and J. Radke, “A 20 bit logarithmic number system
processor,” IEEE Trans. Computers, vol. 37, no. 2, pp. 190-200, 1988.
D. M. Thiboutot, “Dermatological applications of high-frequency ultrasound,” in
Proc. SPIE Med. Imag., vol. 3664, pp. 7-16, 1999.
133
B. G. Tomov and J. A. Jensen, “Compact FPGA-based beamformer using
oversampled 1-bit A/D converters,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr.,
vol. 52, no. 5, pp. 870-880, 2005.
G. E. Trahey, J. W. Allison, S. W. Smith, and O. T. von Ramm, “Speckle pattern
changes with varying acoustic frequency: experimental measurement and
implications for frequency compounding,” in Proc. IEEE Ultrason. Symp., 1986, pp.
815-818.
G. E. Trahey, S. W. Simth, and O. T. von Ramm, “Speckle pattern correlation with
lateral aperture translation: experimental results and implications for spatial
compounding, ” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 33, no. 3, pp.
257-264, 1986.
D. H. Turnbull, T. S. Bloomfield, H. S. Baldwin, F. S. Foster, and A. L. Joyner,
“Ultrsound backscatter microscope analysis of early mouse embryonic brain
development,” in Proc. Natl. Acad. Sci. USA, vol. 92, pp. 2239-2243, 1995.
Y. Wan and C. L. Wey, “Efficient algorithms fro binary logarithmic conversion and
addition,” IEE Proc. Comp. Digit. Tech., vol. 146, no. 3, pp. 168-172, 1999.
D. G. Wildes, R. Y. Chiao, C. M. W. Daft, K. W. Rigby, L. S. Smith, and K. E.
Thomenius, “Elevation performance of 1.25D and 1.5D transducer arrays,” IEEE
Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, no. 5, pp. 1027-1036, 1997.
O. Vainio and Y. Neuvo, “Logarithmic arithmetic in FIR filters,” IEEE Trans.,
Circuits Syst., CAS-33, no. 8, pp. 826-823, 1986.
M. Vogt, H. Ermert, S. el Gammal, K. Kaspar, K. Hoffmann, and P. Altmeyer,
“Structure analysis of the skin using high frequency broadband ultrasound in the
range from 30 to 140 MHz,” in Proc. IEEE Ultrason. Symp., 1998, pp. 1685-1688.
J. E. Volder, “The CORDIC trigonometric computing technique,” IRE Trans.
134
Electron. Comput., vol. 8, pp. 330-334, 1959.
X. –C. Xu, C. –H. Hu, L. Sun, J. T. Yen, and K. K. Shung, “High-frequency high
frame rate ultrasound imaging system for small animal imaging with linear arrays,”
in Proc. IEEE Ultrason. Symp., 2005, pp. 1431-1434.
S. G. Ye, K. A. Harasiewicz, C. J. Pavlin, and F. S. Foster, “Ultrasound
characterization of ocular tissue in the frequency range from 50 MHz to 100 MHz,”
in Proc. IEEE Ultrason. Symp., 1992, pp. 1107-1112.
J. A. Zagzebski, Essentials of Ultrasound Physics, St. Louis, MR: Mosby, 1996.
135
APPENDIX A
ANATOMY OF HUMAN EYE AND HEART
Figure A-1: Anatomy of the human eye
from http://www.pasadenaeye.com/faq/faq15/faq15_text.html
136
Figure A-2: Different cross sectional view of the heart depending on scanning
direction from http://www.rjmatthewsmd.com/Definitions/pop/32cfig.htm.
CW: chest wall, ARVW: anterior right ventricular wall, RV: right ventricle, ISV:
interventricular septum, LV: left ventricle, PLVW: posterior left ventricular,
PPM: posterior papillary muscle, AMVL: anterior mitral valve leaflets, PMVL:
posterior mitral valve leaflets, LAW: left atrial wall, TV: tricuspid valve, AAW:
anterior aortic wall, PAW: posterior aortic wall, AoV: aortic valve, LA: left
atrium, PA: pulmonary artery.
Abstract (if available)
Abstract
High frequency ultrasound is capable of providing fine spatial resolution on the order of several tens of micrometers and fine temporal resolution of more than 200 frames per second. These capabilities are applicable to the cardiac imaging of the mouse where the heart rate is 5-10 beats per second. In order to adequately capture the cardiac activity of the mouse, two key elements are required: high-speed acquisition of echo signals (front-end system) and high-speed signal processing functions to extract clinically useful information from the acquired echo signals and to display the information on a monitor in real time (back-end system).
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Chang, Jin Ho
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Development of back-end processing system for high frequency ultrasound b-mode imaging
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Biomedical Engineering
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2007-12
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