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Novel beamforming techniques for robust contrast enhancement in ultrasound imaging

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Novel beamforming techniques for robust contrast enhancement in ultrasound imaging

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NOVEL BEAMFORMING TECHNIQUES FOR ROBUST CONTRAST ENHANCEMENT IN
ULTRASOUND IMAGING

by

Junseob Shin

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)

March 2014

Copyright 2014 Junseob Shin
II

DEDICATION

To my parents Dong Lip Shin and Ok Hee Kim

III

ACKNOWLEDGMENTS

The past 4 and half years I spent doing my doctoral study was probably the toughest
period of my life in many regards. However, I am very thankful to have gone through this phase
of my life because, as I look back at the past few years I spent here, I realize it was a time for
personal growth and maturity.
I do not consider this thesis as my own achievement, but rather as an achievement of
everyone who was there for me, giving me support, encouragements, friendship, and love. This
thesis would never have been possible without those who have listened to me, prayed for me, and
gave me words of encouragement when I needed them most. I would like to express my gratitude
to those who deserve them:
First and foremost, I would like to thank my doctoral advisor, Dr. Jesse Yen, not only for
his supervision and close guidance on my research, but also for his enormous patience, sense of
responsibility, support, passion and professionalism. Particularly, by setting high standards, he
taught me throughout my study how to be a better thinker with rigor and attention to details. His
work ethic and attitude towards learning and education sets an excellent role model for me and
the lessons he taught me during my study will be more valuable in my career than anything I can
possibly imagine. His teachings will continue to have a positive influence on me throughout my
professional career.
IV

Second, I would like to thank my dissertation committee members who showed great
enthusiasm over my work and provided me support and helpful feedback; Dr.Vasilis Marmarelis,
thank you for being such an awesome teacher with great character, insights, and curiosity. You
have enriched my experience as a graduate student at USC and made it much more exciting and
interesting. Thank you, Dr. Qifa Zhou for giving me constructive feedback on my work and
putting in time and effort to help me continue my journey as a researcher. Thank you, Dr.
Hossein Hashemi for all your compliments, encouragements, and enthusiasm over my work.
Your support kept me motivated and confident.
Third, I would like to give special thanks to my lab mates. Thank you, Man Nguyen for
being not just a lab mate, but a good friend, whom I could share my personal issues and struggles
during the past few years. I cannot imagine how much more difficult my PhD study would have
been without your encouragements and support. Thank you, Yu Chen for helping me out with
hydrophone measurements and for being a good friend as well. Your presence in the lab was a
true blessing for me and made an otherwise solitary endeavor much more pleasant. Also, thank
you, Jay Mung and Yuling Chen for all the helpful discussions we had on my research.
Fourth, I would like to thank my other friends at USC, particularly, Eric Wonjoon Sohn,
Namgyun Lee, and Dongjoon Lee. My experience at USC was more pleasant and exciting than it
would have been without them because they have always encouraged me, challenged me, and
prayed for me.
Fifth, I would like to express my deepest gratitude to my parents in Korea for their
unremitting, unwavering, and unconditional love, consolation and support throughout the past 11
years since I came to the United States. Despite all the financial difficulties, health problems, and
V

other family issues, they consistently showed their faith in me and always encouraged me to
pursue what I believe makes my life meaningful and valuable.
Last but not least, I would like to thank God for His guidance and protection throughout
my study. I have come to deeply understand God’s unconditional love and to experience His
grace and faithfulness in my daily life. Without Him, literally none of my achievements in my
life would have been possible. I praise Him and give all the glory to Him.

VI

TABLE OF CONTENTS

DEDICATION .............................................................................................................................. VI

ACKNOWLEDGMENTS ............................................................................................................ III

TABLE OF CONTENTS .............................................................................................................. XI
LIST OF TABLES ......................................................................................................................... X

LIST OF FIGURES ...................................................................................................................... XI

Chapter 1 Introduction .................................................................................................................... 1

1.1 Motivation ..................................................................................................................... 1
1.2 Background ................................................................................................................... 2
1.3 Literature Review .......................................................................................................... 4
1.3.1 Contrast Enhancement Techniques with Clutter Suppression ....................... 5
1.3.2 Adaptive Imaging Techniques to Restore Coherence .................................... 7

1.4 Scope of Current Work ................................................................................................. 9

1.5 Contributions .............................................................................................................. 10
VII

1.6 Organization of the Dissertation ................................................................................. 11

Chapter 2 Synergistic Enhancements of Ultrasound Image Contrast with Phase Aberration
Correction and Dual Apodization with Cross-Correlation ........................................................... 13

2.1 Introduction ................................................................................................................. 13
2.1.1 Dual Apodizatoin with Cross-correlation .................................................... 13

2.1.2 Limitations of Dual Apodization with Cross-correlation ............................ 16

2.2 Methods....................................................................................................................... 18

2.2.1 Computer Simulations ................................................................................. 18

2.2.2 Experiments in Tissue Mimicking Phantoms .............................................. 20

2.3 Results ......................................................................................................................... 26

2.3.1 Simulation Results ....................................................................................... 26
2.3.1.1 Point Target Simulations ............................................................... 26
2.3.1.2 Anechoic Cyst Simulations ........................................................... 29
2.3.2 Experimental Results ................................................................................... 31
2.3.2.1 Electronic Aberrator Study ........................................................... 31
2.3.2.2 Pork Tissue as Physial Aberrators ................................................ 33
2.4 Discussion ................................................................................................................... 36
2.5 Summary and Conclusion ........................................................................................... 40

Chapter 3 The Effects of Dual Apodization with Cross-Correlation on Tissue Harmonic and
Pulse Inversion Harmonic Imaging in the Presence of Phase Aberration .................................... 42

3.1 Introduction ................................................................................................................. 42
3.1.1 Background .................................................................................................. 42

VIII

3.1.2 Tissue and Pulse Inversion Harmonic Imaging ........................................... 44

3.1.3 Dual Apodization with Cross-correlation .................................................... 46

3.2 Methods....................................................................................................................... 47

3.2.1 Experiments in Tissue Mimicking Phantoms .............................................. 47

3.2.2 Data Processing ............................................................................................ 49

3.3 Results ......................................................................................................................... 53

3.3.1 Experimental Results with Pork Aberrators ................................................ 53

3.4 Discussion ................................................................................................................... 56
3.5 Summary and Conclusion ........................................................................................... 59

Chapter 4 Clutter Suppression Using Phase Apodization with Cross-correlation in Ultrasound
Imaging ......................................................................................................................................... 60

4.1 Introduction ................................................................................................................. 60
4.2 Theory ......................................................................................................................... 62

4.3 Methods....................................................................................................................... 65

4.3.1 Simulation Experiments in Field II .............................................................. 65
4.3.2 DAX and PAX Processing ........................................................................... 66
4.3.3 Experiments with Tissue Mimicking Phantoms .......................................... 68
4.4 Results and Discussion ............................................................................................... 70
4.4.1 Point Target Simulations .............................................................................. 70
4.4.2 Simulated and Experimental Anechoic Cysts .............................................. 72
4.5 Conclusions and Future Work .................................................................................... 74

IX

Chapter 5 Multi Apodization Techniques for Robust Reverberation Clutter Suppression in
Ultrasound Imaging ...................................................................................................................... 75

5.1 Introduction ................................................................................................................. 75
5.2 Methods....................................................................................................................... 78

5.2.1 Multi Apodization Schemes ......................................................................... 78
5.2.1.1 Multi Apodization with Cross-correlation (MAX) ....................... 78

5.2.1.2 Multi Phase Apodization with Cross-correlation (MPAX) .......... 81

5.2.2 Point Target Simulation Experiments in Field II ......................................... 84
5.2.3 Experimental Data from Sponge Phantom .................................................. 85

5.2.4 In-Vivo Evaluation ....................................................................................... 86

5.3 Results and Discussion ............................................................................................... 87

5.3.1 Simulated Beamplots ................................................................................... 87
5.3.2 Sponge Phantom Results ............................................................................. 89
5.3.3 In-vivo Evaluation in Echocardiography ..................................................... 93
5.3.4 In-vivo Evaluation in Abdominal Imaging ................................................ 101
5.4 Conclusions and Future Work .................................................................................. 103

Chapter 6 Conclusions and Future Work ................................................................................... 105

6.1 Conclusions ............................................................................................................... 105

6.2 Future Work .............................................................................................................. 107

6.2.1 Real-time GPU-based beamforming with MAX and MPAX .................... 107

6.2.2 Combination with Spatial Matched Filtering ............................................. 110
BIBLIOGRAPHY ....................................................................................................................... 111

X

LIST OF TABLES

Table 2-1: Field II simulation parameters ..................................................................................... 19

Table 2-2: -6dB beamwidth and 1
st
sidelobe level ........................................................................ 28
Table 2-3: CNR values for simulation and experimental data ...................................................... 35
Table 3-1: Parameters for C4-2 curvilinear array ......................................................................... 48

Table 3-2: Parameters for experimental setup .............................................................................. 49
Table 3-3: CNR values for experimental data .............................................................................. 55
Table 4-1: Field II simulation parameters ..................................................................................... 65
Table 4-2: Summary of CNR values for DAS, DAX, and PAX ................................................... 74

Table 5-1: Field II simulation parameters ..................................................................................... 85

Table 5-2: Summary of CNR values from sponge phantom imaging .......................................... 92

Table 5-3: Summary of CNR values for echocardiography ......................................................... 99
Table 5-4: Summary of CNR values for abdominal imaging ..................................................... 101

XI

LIST OF FIGURES

Figure 1-1: Schematic of standard delay-and sum beamforming in conventional ultrasound
systems. Delays calculated based on path-length differences are applied to a) transmit pulses
from each transmitter to crete a transmit focus, and b) received echo signals from each element
to create a receive focus .................................................................................................................. 4

Figure 1-2: Summary of major contrast enhancement techniques used in ultrasound imaging ..... 8

Figure 2-1: Beamplots for two RX apodizations with 8-8 alternating pattern (RX1 and RX2),
after DAX processing, and DAS for comparison ......................................................................... 16

Figure 2-2: Aberrator profiles of 25ns RMS 5mm FWHM (dashed line) and 45 ns RMS 3 mm
FWHM (solid line) ........................................................................................................................ 19

Figure 2-3: The two 8-8 alternating apodization functions used in DAX .................................... 23

Figure 2-4: A system block diagram for the PAC and DAX combined method .......................... 25

Figure 2-5: Simulated lateral beamplots for (a) DAS, (b) PAC, (c) DAX, and (d) combined PAC
and DAX in the presence of weak (25ns RMS, 5 mm FWHM) aberration .................................. 27

Figure 2-6: Simulated lateral beamplots for (a) DAS, (b) PAC, (c) DAX, and (d) combined PAC
and DAX in the presence of strong (45ns RMS, 3 mm FWHM) aberration ................................ 28

Figure 2-7: Simulated cysts for standard DAS beamforming with uniform apodization and DAX
with (right column) and without (left column) PAC with no aberrator ........................................ 29

Figure 2-8: Simulated cysts for standard DAS beamforming with uniform apodization and DAX
with (right column) and without (left column) PAC in the presence of a weak (25 ns RMS 5mm
FWHM) aberrator ......................................................................................................................... 30

Figure 2-9: Simulated cysts for standard DAS beamforming with uniform apodization and DAX
with (right column) and without (left column) PAC in the presence of a strong (45 ns RMS 3mm
FWHM) aberrator ......................................................................................................................... 30

XII

Figure 2-10: Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with no aberrator ............................ 32

Figure 2-11: Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 25ns RMS 5 mm aberrator .. 32

Figure 2-12: Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 45ns RMS 3 mm aberrator .. 33

Figure 2-13: Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 4 mm pork tissue sample ..... 34

Figure 2-14: Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 10 mm pork tissue sample ... 34

Figure 2-15: Estimated aberrator profiles for a) 4 mm pork and b) 10 mm pork tissue samples . 35

Figure 3-1: The process of forming conventional, tissue harmonic, and pulse inversion harmonic
images with and without DAX ..................................................................................................... 50

Figure 3-2: The 10-10 alternating apodization functions used in DAX ....................................... 51

Figure 3-3: Experimental cysts for conventional imaging at fundamental frequency, tissue
harmonic imaging, and pulse inversion harmonic imaging with (bottom row) and without (top
ropw) DAX with no pork aberrator .............................................................................................. 54

Figure 3-4: Experimental cysts for conventional imaging at fundamental frequency, tissue
harmonic imaging, and pulse inversion harmonic imaging with (bottom row) and without (top
ropw) DAX with a 5 mm pork aberrator ...................................................................................... 54

Figure 3-5: Experimental cysts for conventional imaging at fundamental frequency, tissue
harmonic imaging, and pulse inversion harmonic imaging with (bottom row) and without (top
ropw) DAX with a 12 mm pork aberrator .................................................................................... 54
Figure 3-6: Frequency spectra of the received RF data for left) conventional imaging at
fundamental frequency of 1.96 MHz, center) THI, and right) PIHI at second harmonic ............. 57
Figure 4-1: Aberrator profiles of 25 ns RMS 5 mm FWHM (dashed line) and 45 ns RMS 3 mm
FWHM (solid line) ........................................................................................................................ 66

Figure 4-2: A system diagram for PAX ....................................................................................... 67
Figure 4-3: a) Amplitude and b) phase apodization functions used in DAX and PAX,
respectively ................................................................................................................................... 67

XIII

Figure 4-4: a) Simulated lateral beamplots using complementary phase apodizations (red and
blue) compared with DAS (black). Simulated lateral beamplots are shown for DAS (black),
DAX (blue) and PAX (red) with b) no aberrator, c) a weak (25 ns RMS 5 mm FWHM) aberrator,
and d) a strong (45ns RMS 3 mm FWHM) aberrator ................................................................... 71
Figure 4-5: Simulated cysts for conventional DAS beamforming, DAX, and PAX in the presence
of top) no aberrator, middle) a weak (25 ns 5 mm FWHM) aberrator, and bottom) a strong (45 ns
RMS 3 mm FWHM) aberrator ...................................................................................................... 72
Figure 4-6: Experimental cysts for conventional DAS beamforming, DAX, and PAX in the
presence of top) no aberrator, middle) a weak (4 mm pork) aberrator, and bottom) a strong (10
mm pork) aberrator ....................................................................................................................... 73
Figure 5-1: 4-4 alternating DAX apodization functions ............................................................... 79
Figure 5-2: MAX (N=4) apodization functions ............................................................................ 79
Figure 5-3: Diffraction efficiency 𝐽
!
!
𝑚 2 vs. m/2 for three values of grating order q ............. 82
Figure 5-4: Examples of complementary sinusoidal phase apodizations used in PAX and MPAX.
Sinusoidal time delays with 3 different f
0
values are shown for m=3.6 rad: top) f
0
= 342 cycles/m,
middle) f
0
= 391 cycles/m, and bottom) f
0
= 635 cycles/m ........................................................... 83
Figure 5-5: Simulated lateral beamplots for a) 4-4 dax, b) MAX (N = 4), and c) PAX and MPAX
....................................................................................................................................................... 88
Figure 5-6: Experimental results from a custom sponge phantom without a copper wire mesh for
standard DAS beamforming and the 4 processing methods ......................................................... 89
Figure 5-7: Experimental results from a custom sponge phantom with a copper wire mesh for
standard DAS beamforming and the 4 processing methods ......................................................... 90
Figure 5-8: Final normalized cross-correlation coefficient matrices obtained without a copper
wire mesh for the 4 processing methods ....................................................................................... 91
Figure 5-9: Final normalized cross-correlation coefficient matrices obtained with a copper wire
mesh for the 4 processing methods ............................................................................................... 92
Figure 5-10: In-vivo images of an apical four-chamber view at end-systole for standard DAS
beamforming and the 4 processing methods ................................................................................. 94
Figure 5-11: In-vivo images of an apical four-chamber view at end-diastole for standard DAS
beamforming and the 4 processing methods ................................................................................. 94
Figure 5-12: Final normalized cross-correlation coefficient matrices of an apical four-chamber
view at end-systole for the 4 processing methods ........................................................................ 95
XIV

Figure 5-13: Final normalized cross-correlation coefficient matrices of an apical four-chamber
view at end-diastole for the 4 processing methods ....................................................................... 96
Figure 5-14: In-vivo images of a subxiphoid view at end-systole for standard DAS beamforming
and the 4 processing methods ....................................................................................................... 97
Figure 5-15: In-vivo images of a subxiphoid view at end-diastole for standard DAS beamforming
and the 4 processing methods ....................................................................................................... 97
Figure 5-16: Final normalized cross-correlation coefficient matrices of a subxiphoid view at end-
systole for the 4 processing methods ............................................................................................ 98
Figure 5-17: Final normalized cross-correlation coefficient matrices of a subxiphoid view at end-
diastole for the 4 processing methods ........................................................................................... 98
Figure 5-18: Mean a) contrast, b) contrast-to-noise ratio (CNR) and c) speckle signal-to-noise
ratio (speckle SNR) calculated in 18 frames of MAX images as a function of the L value. ...... 100
Figure 5-19: In-vivo standard DAS and MAX images of an apical four-chamber view at end-
systole with L = 1, 3, and 10 ....................................................................................................... 100
Figure 5-20: In-vivo long-axis view images of the abdominal aorta for standard DAS
beamforming and the 4 processing methods ............................................................................... 102
Figure 5-21: Final normalized cross-correlation coefficient matrices of a long-axis view of the
abdominal aorta for the 4 processing methods ........................................................................... 102
Figure 6-1: The work flow for real-time GPU-based software beamforming with MAX or MPAX
..................................................................................................................................................... 109

1

Chapter 1 Introduction
1.1 Motivation
Ultrasound is one of the most widely used imaging modalities in clinics today and has
been proven useful in visualizing anatomical structures of the human body. Although it provides
images with high spatial resolution, ultrasound often suffers from poor contrast and hence,
makes identification of targets such as blood vessels, cysts, tumors, and visualization of heart
chambers difficult (Rubin et al, 2000). This is mainly because the contrast-to-noise ratio (CNR)
and image resolution are degraded by off-axis sidelobes and clutter inherent in conventional
delay-and-sum (DAS) beamforming used in array systems.
Improving ultrasound image contrast may have a direct impact on many physicians and
patients, as there are numerous clinically significant applications. In echocardiography, a high
quality, high contrast image is a valuable diagnostic imaging tool from which patients benefit
significantly. However, visualizing heart chambers and nearby blood vessels often becomes very
difficult especially with large patients who generate high phase aberration effects. Also, high
image contrast is particularly important for breast ultrasound, which focuses on identifying solid
and cystic masses (Basset et al, 1997). Misdiagnosis of simple anechoic cysts with fill-in due to
reverberations, multiple scattering, and clutter as malignant lesions is common and identification
of these anechoic cysts becomes even more challenging with increased levels of fill-in caused by
2

phase aberrations from thick fat and tissue layers. In abdominal ultrasound, imaging of
gallbladder stones and polyps, assessment of thrombus or plaque in the aorta, solid organ and
transplant vasculature, and differentiation between simple cysts, complicated cysts, and solid
nodules within organs such as liver, spleen and pancreas may benefit from improved image
contrast. Other areas of relevance include hepatic imaging (Semelk, 2005) and imaging of
prostate cancer which is known to be hypoechoic (Lee et al, 1989).
1.2 Background
In array ultrasound systems, a pulse-echo B-mode image is obtained through a process
known as beamforming, in which electronic focusing of the acoustic beam is achieved in both
transmit and receive. The standard beamforming method in ultrasound imaging is delay-and-sum
(DAS) beamforming as shown in Fig 1-1. On transmit, DAS beamforming aims to focus all the
available acoustic energy and achieve a large-amplitude signal at the intended focal point by
transmitting pulses from individual array elements with appropriate time delays calculated based
on the distances between the array element locations and the focal point (Fig 1-1a). The time
delay for the n
th
element 𝜏
!
can be calculated using the following equation:

𝜏
!
=
!!
!
!
(1.1)

3

where c is the average sound speed typically assumed to be 1540 m/s in the human body and Δ𝑟
!

is the difference in the distances between the n
th
element to the focus and the farthest element to
the focus.
Similarly, on receive, DAS beamforming aims to achieve a large-amplitude signal from
the focal point by applying appropriate time delays to echo signals received by individual array
elements and summing them up. In an ideal case where an infinitely long aperture may be used,
it is theoretically possible to focus all the available acoustic energy at a single location and avoid
any sidelobes. However, as briefly mentioned earlier, the inherent limitation in current
ultrasound imaging systems is that sidelobes and clutter signals arising from off-axis targets that
degrade spatial and contrast resolutions are unavoidable because of the finite aperture size, which
is often constrained by the human anatomy and hardware limitations. In addition, the accuracy of
DAS beamforming and hence, the quality of the acoustic beam, in terms of the beamwidth and
sidelobe level depends on the validity of the assumption that sound speed in the human body is
1540 m/s. Previous studies have shown that sound speed may deviate from the assumed value by
up to 10% depending on the body composition of the patient (Goss et al, 1978), and causes
further degradation in image quality in terms of both spatial and contrast resolutions.

4

Fig. 1-1. Schematic of standard delay-and-sum beamforming in conventional ultrasound systems.
Delays calculated based on path-length differences are applied to a) transmit pulses from each
transmitter to create a transmit focus, and b) received echo signals from each element to create a
receive focus.
1.3 Literature Review
A number of techniques including apodization, spatial compounding, and frequency
compounding were proposed in the past as solutions to reduce undesirable side effects of DAS
beamforming and achieve an improvement in ultrasound image contrast, but at the expense of
increased computational burden, worse lateral resolution or frame rate (Shankar, 1986; Forsberg
et al, 1991; Rigby, 2000). Given that the ideal contrast enhancement technique would achieve a
great level of contrast improvement with no penalty in spatial or temporal resolution and
5

increased computational complexity, a number of such techniques have been reported in
literature over a period of approximately 25 years. These methods may be broadly classified into
two groups: 1) methods that aim to suppress the effects of focusing errors and clutter by
developing and applying a target-dependent weighting matrix to the beamformed RF data and 2)
methods that aim to restore coherence by estimating and correcting for focusing errors that cause
degradation in image quality. Fig 1-2 summarizes major contrast enhancement methods to date.

1.3.1 Contrast enhancement techniques with clutter suppression
The most popular approach employed in the first group of imaging techniques is
developing a weighting matrix based on the coherence of the received RF data. The coherence
factor (CF), which was first introduced in 1999 (Hollman et al, 1999) uses the ratio of the
coherent energy to the total incoherent energy of the received RF data to weight each image
point at every depth. Generalized Coherence Factor (GCF) was developed by modifying CF to
account for the energy spread by speckle-generating targets that CF does not take into
consideration (Li and Li, 2000). Since the received RF signals from the mainlobe region are
coherent and correspond to low frequency components, whereas those from sidelobe and clutter
are incoherent and correspond to high-frequency components, GCF is computed as a ratio of the
spectral energy within a low frequency region to the total spectral energy. A matrix of GCF
values is then used to weight each pixel within the field-of-view (FOV). Phase coherence factor
(PCF) and sign coherence factor (SCF) proposed in 2009 employ a sidelobe reduction approach
6

similar to GCF, but the matrix for pixel-by-pixel weighting is based on phase diversity of the
delayed channel RF signals across the aperture rather than coherence (Camacho et al, 2009). The
parallel adaptive receive compensation algorithm (PARCA) and its modified version, PARCA2,
on the other hand, aim to estimate aberration effects by modeling them as off-axis scatterers
insonified by a distorted transmit beam (Li et al, 1993; Krishnan et al, 1998). Then, the signals
coming from these modeled off-axis scatterers can be iteratively estimated and compensated
from the on-axis signal.
There is also a family of nonlinear sidelobe suppression techniques that are based on
aperture apodizations. Spatially variant nonlinear apodization (SVA) proposed in 1995 takes
advantage of the lateral phase differences between uniform and Hanning apodizations to identify
and suppress clutter signals. SVA finds the optimal aperture domain apodization function from a
continuum of possible apodization functions for each pixel in an image by taking advantage of
the properties of raised-cosine functions (Stankwitz et al, 1995). Minimum variance
beamforming (MVBF) first proposed in 1969 for narrowband applications (Capon, 1969)
employs an adaptive apodization scheme that depends on the statistics of the received signals to
overcome the limitation of conventional apodization techniques, which is a trade-off in mainlobe
width in order to reduce sidelobe levels. MVBF achieves reduction in both mainlobe width and
sidelobe level by suppressing off-axis signals and allowing large sidelobes in directions where no
energy is received. Extensions of MVBF technique for broadband applications were developed
and were recently demonstrated to be feasible with ultrasound imaging (Mann and Walker, 2002;
Sasso and Cohen-Bacrie, 2005; Synnevag et al, 2005), but at the expense of higher
computational burden. More recently, another method called the short-lag spatial coherence
7

(SLSC) was introduced (Dahl et al, 2011). Unlike conventional B-mode imaging that forms
images based on echo brightness, SLSC forms images similar to conventional B-mode images
using lateral spatial coherence as the basis. Each pixel in such images is generated by computing
the SLSC value, V
slsc
at every axial depth from the spatial coherence function and the SLSC
integral. Although shown to have some promising results, computation of the SLSC value at
every pixel is extremely computationally heavy. Furthermore, SLSC is unable to detect point-
like targets in speckle-based background as the coherence of speckle cannot be distinguished
from that of the point target for short lags (Lediju et al, 2011). Hence, SLSC is inappropriate for
clinical applications which depend on point target conspicuity, such as microcalcification
detection.
1.3.2 Adaptive imaging techniques to restore coherence
Among the latter group of contrast enhancement methods, the nearest-neighbor cross-
correlation (NNCC) method was the first to be proposed in 1988 (Flax and O’Donnell, 1988).
This method performs cross-correlation of neighboring RF signals to calculate relative time
shifts, from which the phase aberrator profile across the transducer surface may be obtained. The
focusing errors depicted by the estimated phase aberrator profile are then compensated for by
time-shifting individual channel RF signals. Iteration of such a procedure is necessary in order to
achieve enhanced focusing quality of the transmit beam that has been distorted by the phase
aberration. Another method based on maximization of speckle brightness rather than channel-to-
channel correlation of RF signals was introduced in 1989 (Nock et al, 1989). Because the speckle
8

brightness is directly related to the focusing quality, any degradation of the beam due to phase
aberration results in a reduced average speckle brightness in the image. Hence, the goal of this
method is to correct focusing errors by delaying individual channel RF signals to achieve
maximal speckle brightness in the image. Other methods include time-shift compensation based
on element-to-beamsum correlations (Rigby, 1995), backpropagation of the received pressure
field (Liu and Waag, 1994), and time reversal focusing (Mallart and Fink, 1994).

Fig. 1-2. Summary of major contrast enhancement techniques used in Ultrasound Imaging.

9

1.4 Scope of current work
This dissertation presents an adaptive clutter suppression technique called dual
apodization with cross-correlation (DAX). This method takes advantage two distinct receive (RX)
aperture weighting functions to distinguish between signals coming from the mainlobe and those
coming from sidelobes and clutter. Compared to other clutter suppression techniques surveyed
above, the most important distinctive feature of DAX is that it achieves large improvements in
image contrast without much additional computational power. This reduces complexity and
computational burden and makes implementation real-time feasible.
On the other hand, the major limitation of this technique is the decrease in its
performance and its tendency to create image artifacts with increased levels of phase aberration
that causes degradation of the beam focusing quality. The goal of this work is to show that the
limitations of DAX can be overcome and that the performance can be improved significantly by
pursuing either an integration with other imaging techniques or modifications to the DAX
algorithm itself. I attempt to demonstrate in this dissertation that DAX with such
accommodations has great potentials for enhanced ultrasound image contrast in numerous
clinical imaging applications.

10

1.5 Contributions
My Ph.D. study has resulted in a number of peer-reviewed publications. They include
two journal articles, two conference papers, two conference abstracts, a co-authored journal
article, and a co-authored conference paper:

Journal Articles
Nguyen M., Shin J., and Yen J. T., “Harmonic Imaging with Fresnel beamforming in the
presence of phase aberration,” Ultrasound in Medicine and Biology, In Press.

Shin J., and Yen J. T., “Effects of dual apodization with cross-correlation on tissue harmonic
and pulse inversion harmonic imaging in the presence of phase aberration,” IEEE Trans.
Ultrason. Ferroelectr. Freq. Control, vol. 60, no. 3, pp.643-649, Mar. 2013.

Shin J., and Yen J. T., “Synergistic enhancements of ultrasound image contrast with a
combination of phase aberration correction and dual apodization with cross-correlation,” IEEE
Trans. Ultrason. Ferroelectr. Freq. Control, vol. 59, no. 9, pp.2809-2101, Sep. 2012.

Conference Papers and Abstracts
Shin J., and Yen J. T., “Clutter suppression using phase apodization with cross-correlation in
ultrasound imaging,” IEEE International Ultrasonics Symposium Proceedings, Prague, July 21-
25, 2013.

Shin J., and Yen J. T., “A new approach to enhance ultrasound image contrast: an ex vivo
validation study,” BMES Annual Meeting, San Diego, August 28- September 1, 2012.

Shin J., and Yen J. T., “Performance evaluation of an integrated ultrasound image contrast
enhancement technique for cardiac imaging,” EMBC, San Diego, August 28- September 1, 2012.

Shin J., and Yen J. T., “Improved image quality using phase aberration correction and dual
apodization with cross-correlation,” IEEE International Ultrasonics Symposium Proceedings,
Orlando, October 18-21, 2011.

11

Nguyen M., Shin J., and Yen J. T., “Fresnel beamforming and dual apodization with cross-
correlation for curvilinear arrays in low-cost portable ultrasound system,” IEEE International
Ultrasonics Symposium Proceedings, Orlando, October 18-21, 2011.

1.6 Organization of the dissertation
This dissertation is organized into 6 chapters:

Chapter 1 provides a brief background on ultrasound imaging with an emphasis on
beamforming for array ultrasound systems. It also describes the motivation of this work and
surveys major existing techniques for ultrasound contrast enhancement.

Chapter 2 describes Dual Apodization with Cross-correlation and presents its performance
evaluation. It also presents improvements in its performance when it is combined with a phase
aberration correction technique based on nearest-neighbor cross-correlation (NNCC) of channel
RF data. Such a combined approach helps overcome the inherent limitations of DAX and
achieves synergistic enhancements of ultrasound image contrast.

Chapter 3 presents improved performance of DAX with tissue harmonic imaging (THI) and
pulse inversion harmonic imaging (PIHI), which are based on nonlinear acoustic wave
propagation. The results show that reduced effects of phase aberration with THI and PIHI help
DAX significantly in suppressing clutter and achieve improvements in image contrast beyond
what DAX, THI, or PIHI alone could achieve.
12

Chapter 4 presents an extension of DAX called Phase Apodization with Cross-correlation
(PAX), which takes advantage of grating lobes due to sinusoidal phase delays in channel RF data.
Initial results from simulation and tissue-mimicking phantom are presented for performance
evaluation.

Chapter 5 presents Multi Apodization with Cross-correlation (MAX) and Multi Phase
Apodization with Cross-correlation (MPAX), which are extensions of DAX and PAX,
respectively for increased robustness, particularly for in-vivo imaging. Although similar to DAX
in terms of the operations being utilized, MAX takes advantage of larger grating lobe magnitude
and the additional phase diversity from multiple apodization pairs. MPAX also takes advantage
of the increased flexibility of PAX in manipulating grating lobe magnitudes and locations to
obtain multiple measurements from which a more reliable weighting factor can be derived. The
performance of MAX and MPAX is evaluated with simulation, experiment, and in-vivo for
echocardiography and abdominal imaging.

Chapter 6 summarizes and concludes the dissertation and proposes future work.

13

Chapter 2 Synergistic Enhancements of Ultrasound Image
Contrast with Phase Aberration Correction and Dual
Apodization with Cross-Correlation

2.1 Introduction
In this chapter, the concept of dual apodization with cross-correlation as a clutter
suppression method is first presented. This method is originally motivated by Stankwitz et al
(Stankwitz et al, 1995), whose work showed that by taking the minimum of two RX apodization
functions - one with uniform apodization and the other with Hanning apodization, it is possible
to achieve lower sidelobes without compromising resolution. In addition, the diminishing
performance of DAX with different levels of phase aberration is shown and a solution to
overcome this problem is proposed.
2.1.1 Dual Apodization with Cross-correlation
Since any ultrasound echo signal can be treated as a combination of one signal from
mainlobe and another signal from clutter, DAX aims to improve ultrasound image contrast by
first differentiating clutter signals from mainlobe-dominated signals and then minimizing their
14

contributions to the ultrasound echo signal. Instead of a single receive (RX) apodization utilized
in conventional DAS beamforming, DAX uses two distinct RX apodizations to generate two
different point spread functions having similar mainlobe signals but very different clutter
patterns. Since DAX does not require a second apodization on transmit, there is no loss of frame
rate. By means of normalized cross-correlation between beamformed RF signals from the two
different RX apodizations at zero lag, followed by a thresholding operator, a weighting matrix
composed of cross-correlation coefficients ranging from the threshold value 𝜀=0.001 and 1 is
created:

𝜌 𝑙,𝑚 =
𝑅𝑋1 𝑘,𝑚 𝑅𝑋2(𝑘,𝑚)
!!!!!
!!!!!
𝑅𝑋1(𝑘,𝑚)
! !!!
!!!
𝑅𝑋2(𝑘,𝑚)
! !!!
!!!
(2.1)

where l is the l
th
sample on image line m with a cross-correlation segment length of 2A+1
samples. Since mainlobe-dominated signals are highly correlated, coefficients associated with
these signals are close to 1. Uncorrelated clutter signals have coefficients close to the threshold
value. By multiplying the resulting weighting matrix by the combined RF data, DAX achieves a
dramatic improvement in image contrast by attenuating signals dominated by clutter.
There are several pairs of apodization functions that generate a well-correlated mainlobe
response and an uncorrelated sidelobe response. Such pairs include 1) uniform and Hanning, 2) a
pair of uniform apodization functions with a fractional translation of the active subaperture that
have a common midpoint, 3) a pair of randomly selected apodization functions that are
complementary to one another, and 4) a set of two complementary apodization functions with N
15

alternating elements enabled on one but disabled on the other. Based on the investigation
described previously (Seo and Yen, 2008a), the best performance in terms of image contrast
improvement was achieved with the fourth apodization scheme where two complementary
alternating apodization functions are utilized. Such a set of complementary apodization functions
may be regarded as arrays having an effective pitch equivalent to 2×𝑁×𝑔 where g is the pitch or
the interelement distance. Since the n
th
grating lobe angle is given by:

𝜃
!
= sin
!!
!"
!
(2.2)

where 𝜆 is the ultrasound wavelength, the grating lobes with the N-alternating apodization
scheme are now located at a distance d
g
away from the center of the main beam when the beam
is focused at a distance d
f
away from the transducer surface:

𝑑
!
= 𝑑
!
×tan sin
!!
!"
!×!×!
(2.3)

For example, the two complementary apodization pairs depicted in Fig. 2-1 place grating lobes at
roughly ±1.9 mm away from the center of the mainlobe at a focal depth of 30 mm. Since the
first grating lobes are 180
o
out of phase with each other, the two complementary alternating
apodization functions generate beamsums that result in a normalized cross-correlation coefficient
near -1 if the signals are coming from the grating lobe region. On the other hand, signals
16

originating from the mainlobe region are highly correlated and generate normalized cross-
correlation coefficient of near 1.

Fig. 2-1. Beamplots for two RX apodizations with 8-8 alternating pattern (RX1 and RX2), after
DAX processing and DAS for comparison.

Therefore, although grating lobes are widely considered undesirable as they could degrade the
image contrast and create artifacts that may lead to misdiagnosis, DAX with an alternating
apodization scheme is unique in that it purposefully introduces and aims to benefit from such
undesirable grating lobes by assessing the phase differences in the beamsum signals.

2.1.2 Limitations of Dual Apodization with Cross-correlation
Previously, DAX was shown to achieve contrast improvement of 139% in simulation and
123% experimentally without sacrificing either lateral or axial resolution (Seo and Yen, 2008a).
In a follow-up study, the robustness of DAX was evaluated in the presence of different levels of
17

aberration and signal-to-noise ratios (SNR) (Seo and Yen, 2009). It was shown that although the
performance of DAX is highly robust in minimizing effects of weak- and medium-strength phase
aberrations, a decrease in CNR improvement and lesion visibility was observed in both
simulation and experiment as the aberration strength was increased (Seo and Yen, 2009). In
addition, simulation results showed that DAX had a tendency to cause distortions in the target
shapes and create image artifacts in the surroundings with increased aberration strength, which
could lead to misdiagnosis (Seo and Yen, 2009).
To address the challenges in ultrasonic imaging posed by phase aberration, a segment of
ultrasound imaging community has developed methods to restore the image quality lost due to
aberration. Unlike DAX, which operates by minimizing the undesirable aberration effects on
image quality, phase aberration correction (PAC) attempts to restore coherence by estimating
and correcting phase errors caused by sound speed inhomogeneities in tissue. As surveyed in
Chapter 1 of this document, there are a number of aberration estimation and correction methods
including time shift compensation based on element-to-element (Flax and O’Donnell, 1988) or
element-to-beamsum correlations (Rigby, 1995), backpropagation of the received pressure field
(Liu and Waag, 1994), time reversal focusing (Mallart and Fink, 1994), and speckle brightness as
a quality factor (Nock et al, 1989). Previous studies have shown that PAC methods based on
near-field phase screen models use element-to-element or element-to-beamsum correlations.
Such methods, though shown to be promising, exhibit limitations, including increased
computational burden and reduced frame rate, as they are often iterative in nature. The accuracy
in estimating aberration profiles also decreases with increasing aberration strength and
correlation lengths.
18

Although both DAX and PAC showed decreased performance with increasingly strong
aberrations, one way to maximize improvements in image quality is to use a combined approach
in which phase correction on individual channel RF signals is followed by DAX on the phase
corrected, beamformed RF signals. Since the contrast enhancement mechanisms of DAX and
PAC are different, it is expected that the two methods, when integrated, will generate synergistic
effects that will increase contrast beyond that achievable by DAX alone or PAC alone. This
paper proposes integration of DAX with a NNCC-based PAC method described by O’ Donnell et
al (O’Donnell and Flax, 1988; O’Donnell and Engeler, 1992) and examines its performance in
terms of image resolution and contrast.

2.2 Methods
2.2.1 Computer Simulations
Computer simulations for a point target and an anechoic cyst were performed using Field
II (Jensen, 1992) to compare the performance of the proposed method with that of DAX alone
and PAC alone in terms of lateral beamwidth and image contrast. The imaging parameters used
are summarized in Table 2-1. To simulate the effects of aberrating layers on the beam, zero-
mean, random electronic near-field phase screens were generated by convolving Gaussian
random numbers with a Gaussian function as described by Dahl et al (Dahl et al, 2005). 25ns
RMS 5mm full-width half-maximum (FWHM) and 45ns RMS 5mm FWHM aberrator profiles
19

were created as shown in Fig. 2-2, and applied on both transmit and receive for point target and
anechoic cyst simulations.

TABLE 2-1. Field II Simulation Parameters

Fig. 2-2. Aberrator profiles of 25 ns RMS 5mm FWHM (dashed line) and 45 ns RMS 3mm FWHM
(solid line).

For anechoic cyst simulations, images of a 3mm-diameter cylindrical cyst located at a
depth of 30 mm were generated and image contrast was assessed for standard DAS beamforming,
DAX alone, PAC alone, and DAX combined with PAC in the presence of weak and strong
aberrators using the equation for contrast-to-noise ratio (CNR) (O’Donnell and Flax, 1988):
Parameters Value
Number of Elements in Subaperture 64
Center Frequency
Bandwidth
5 MHz
50 %
Azimuthal Element Pitch 305 µm
Elevation Element Height
Sound Speed
Transmit Focus
Lateral Beam Spacing (Point target)
Lateral Beam Spacing (Cyst)
5 mm
1540 m/s
30 mm
100 µm
150 µm
Receive focal delay step 0.1 mm
1
20

𝐶𝑁𝑅=
𝑆
!
− 𝑆
!
𝜎
!
(2.4)

where 𝑆
!
is the mean of the target, 𝑆
!
is the mean of the background and 𝜎
!
is the standard
deviation of the background of the envelop-detected, log compressed image in dB.

2.2.2 Experiments in Tissue Mimicking Phantoms
To validate the results from computer simulations, imaging experiments with both
electronic and physical aberrators were performed. Full synthetic aperture radio frequency (RF)
data sets were acquired from an ATS ultrasound phantom (ATS laboratories, Bridgeport, CT,
Model 549) containing 3 mm-diameter anechoic cysts located at 30 mm in depth and sampled at
45 MHz for offline processing. This serves as the control data set for comparison and it was also
used to generate data sets with electronic aberrators by applying the aberrator profiles shown in
Fig. 2-2 on both transmit and receive. To mimic near-field aberrating layers composed of skin,
muscle, and fat commonly encountered in clinical ultrasound imaging, tissues of thickness 4 mm
and 10 mm from pork belly were placed in between the transducer and the ATS cylindrical
lesion phantom. These RF signals were collected using a Verasonics data acquisition system
(Verasonics, Redmond, WA) with a 128–element, 298 µm pitch L7-4 linear array. A 1-cycle
transmit pulse with a center frequency of 5 MHz and a subaperture size of 64 elements were used.
21

Data from each channel were collected 12 times and averaged to minimize the effects of
electronic noise. All individual channel RF signals were band-pass filtered using a 64-tap finite
impulse response (FIR) band-pass filter with frequency range limited to the -6 dB bandwidth of
the transducer and low-pass interpolated by a factor of 4 to achieve finer delay quantization and
estimation. Offline beamforming was then performed using Matlab (The MathWorks, Inc. Natick,
MA) with a constant f-number of 2. For control and electronically aberrated data sets, the
transmit focus was always set to a depth of 30 mm where a 3 mm-diameter anechoic cyst is
located, but it was moved down by the thickness of the pork tissue in the presence of pork belly.
Dynamic receive focusing was used with focal updates every 1 mm in range and an image line
spacing of 100 µm.

Phase Aberration Correction
The NNCC-based phase aberration correction algorithm was implemented as described
by O’ Donnell et al (O’Donnell and Flax, 1988; O’Donnell and Engeler, 1992). The cross-
correlation function between any two neighboring elements with channel RF signals x(n) and y(n)
was calculated as:

𝐴 𝑘 = 𝑥 𝑛 𝑦 𝑛+𝑘
!
!
!!
!
!
!
2.5

where M represents the total number of samples which contribute to the cross-correlation
function A(k). The cross-correlation function was computed for every channel over a segment
22

length of 13 mm centered at the transmit focus, which is equivalent in wavelengths to what was
used by O’Donnell and Flax at a center frequency of 3.3 MHz (O’Donnell and Flax, 1988). The
differential delay error between all neighbors was then calculated by computing the time shift
between two neighboring elements that results in maximal normalized cross-correlation
coefficient. The delay error at any channel n > 0 in the N-element subaperture (N = 64) was
computed by unwrapping the differential time delays and removing any unwanted linear
component using the following equation:

𝛥𝜏
!
= 𝛥𝑡
!
−𝑛
!!!
!!!
𝛥𝑡
!
!!!
!!!
𝑁−1
2.6

where Δτ
!
= 0 is selected for n = 0. For all simulated and experimental data sets presented in
this paper, the estimated phase error on every channel was corrected on both transmit and receive.

DAX
For all results shown in this study, an 8-8 alternating pattern, in which a set of two
complementary apodization functions with 8 alternating elements are enabled on one but
disabled on the other, was selected as it has been shown to achieve the greatest CNR
improvement without creating undesirable black artifacts near the transmit focus in the presence
of diffuse scatterers (Seo and Yen, 2009). The two receive apodization functions for DAX are
shown in Fig. 2-3. Use of such apodization functions on the receive aperture creates grating
lobes that are 180 degrees out of phase with respect to one another such that the mainlobe-
23

dominated signals can be distinguished from clutter signals by means of normalized cross-
correlation.
A segment of 2 wavelengths was empirically chosen for zero-lag, normalized cross-
correlation (NCC) between the two beamformed RF signals obtained with the two
complementary apodization functions. To minimize the artifacts in the form of black spots which
may arise due to the random nature of speckle, the weighting matrix composed of normalized
cross-correlation coefficients ranging from ε = 0.001 to 1 after thresholding was median filtered
with a window size of 0.6 mm × 1.2 mm. The size of the median filter was also empirically
selected such that the effect of most artifacts is removed with minimal blurring of the weighting
matrix.

Fig. 2-3. The two 8-8 alternating apodization functions used in DAX.

24

The Combined Method
The PAC and DAX combined method proposed in this paper is demonstrated in Fig. 2-4.
The two block diagrams labeled as PAC and DAX summarize the details and steps of each
method described in the previous sections. PAC was first applied on the RF data which had been
delayed with geometric delay profiles calculated based on array geometry to gain increased
coherence of the beam. For all simulation and experimental data presented in this paper, phase
correction was first performed on transmit using phase error estimates from receive and then on
receive using phase error estimates obtained with a corrected transmit beam. Next, DAX was
performed to suppress any sidelobes and clutter.
25

Fig. 2-4. A system block diagram for the PAC and DAX combined method.

26

2.3 Results
2.3.1 Simulation Results
2.3.1.1 Point Target Simulations
The performance of the NNCC-based PAC method, DAX, and the combined method for
weak and strong aberrators are depicted by lateral beamplots in Figs 2-5 and 2-6, respectively. In
all figures, the lateral beamplot for standard DAS beamforming with uniform apodization in the
absence of an aberrator is shown as a control. The -6 dB beamwidth and first sidelobe level for
DAS and DAX with and without PAC for no, weak (25ns RMS 5mm FWHM) and strong (45 ns
RMS 3mm FWHM) aberrations are summarized in Table 2-2.
Fig. 2-5 shows lateral beamplots for different processing methods in the presence of weak
aberration. The aberration resulted in an increase in sidelobe level from -29.2 dB to -8.6 dB for
DAS beamforming with no DAX or PAC (Fig. 2-5a). Although DAX successfully suppressed
most of clutter down to -80 dB or lower, the high sidelobes near the mainlobe still remain (Fig.
2-5c). However, PAC proved to be useful in lowering the high sidelobes, which DAX failed to
suppress, down to -20 dB (Fig. 2-5b). Finally, with the help of PAC, DAX was able to achieve
additional sidelobe suppression of 10.1 dB near the mainlobe and yield a beam comparable to or
even better than the control in terms of -6 dB beamwidth and first sidelobe level (Fig. 2-5d). This
is possible because PAC reduces the high sidelobes that DAX fails to suppress.
27

Fig. 2-5. Simulated lateral beamplots for (a) DAS, (b) PAC, (c) DAX, and (d) combined PAC and
DAX in the presence of weak (25ns RMS, 5 mm FWHM) aberration.

Similar patterns were observed in the case of a strong aberrator as shown in Fig. 2-6. The
-6 dB beamwidth was increased and the sidelobes were raised to 0 dB with conventional DAS
beamforming (Fig. 2-6a). Again, DAX was not able to suppress the high sidelobes located
approximately 1 mm away from the main lobe (Fig. 2-6c). PAC, on the other hand, lowered
these high sidelobes by 29.6 dB. Moreover, a reduction of at least 10 dB was observed with
clutter signals farther away from the mainlobe (Fig. 2-6b). Finally, the combined PAC and DAX
resulted in a beam with sidelobes much lower than what DAX alone or PAC alone could achieve
and beamwidth comparable to that obtained by PAC alone (Fig. 2-6d).

28

Fig. 2-6. Simulated lateral beamplots for (a) DAS, (b) PAC, (c) DAX, and (d) combined PAC and
DAX in the presence of strong (45ns RMS, 3mm FWHM) aberration.

TABLE 2-2. -6dB Beamwidth and 1
st
Sidelobe Level

-6 dB beamwidth and first sidelobe level from Field II point target simulations with weak (25 ns
RMS 5 mm FWHM) and strong (45ns 3 mm FWHM) aberrators are shown for DAS beamforming
and DAX with and without PAC. The beamwidth and first sidelobe level for DAS beamforming
with no aberrator were 0.45 mm and -29.2 dB, respectively and serve as a control for comparison.
29

2.3.1.2 Anechoic Cyst Simulations
Anechoic cysts simulated with no, weak and strong aberrators are shown on a 50 dB
dynamic range in Figs 2-7, 2-8 and 2-9, respectively. CNR values were calculated and
summarized in Table 2-3. For each aberration, CNR values for standard DAS beamforming, and
DAX were calculated with and without PAC. CNR values with no aberrator were used as a
control. Standard DAS beamforming yielded a progressive decrease in CNR from 5.21 with no
aberrator, to 4.10 with a weak aberrator, and to 1.69 with a strong aberrator. DAX yielded CNR
improvements of over 80% in all three cases while PAC achieved improvements of 0.6% for no
aberrator, 23.9% for a weak aberrator, and 176.3% for a strong aberrator. The combined method
always achieved the best results with CNR values of 10.72 for no aberrator, 10.96 for a weak
aberrator, and 9.80 for a strong aberrator.

Fig. 2-7. Simulated cysts for standard DAS beamforming with uniform apodization and DAX with
(right column) and without (left column) PAC with no aberrator.

30

Fig. 2-8. Simulated cysts for standard DAS beamforming with uniform apodization and DAX with
(right column) and without (left column) PAC in the presence of a weak (25 ns RMS 5mm FWHM)
aberrator.

Fig 2-9. Simulated cysts for standard DAS beamforming with uniform apodization and DAX with
(right column) and without (left column) PAC in the presence of a strong (45ns RMS 3mm FWHM)
aberrator.
31

2.3.2 Experimental Results
2.3.2.1 Electronic Aberrator Study

Figs 2-10, 2-11, and 2-12 show the experimental images of the ATS tissue-mimicking
phantom containing anechoic cysts with no, weak (25ns RMS, 5mm FWHM), and strong (45ns
RMS, 3mm FWHM) electronic aberrators. All images are shown on a 50 dB dynamic range.
CNR values are calculated as done for simulation data and summarized in Table 2-3. Similar to
the trends shown by the anechoic cyst simulations, standard DAS beamforming yielded a
progressive decrease in CNR from 5.36 with no aberrator, to 4.04 with a weak aberrator, and to
2.20 with a strong aberrator. DAX yielded CNR improvements of 90.7% for no aberrator and
80.9% for a weak aberrator, but resulted in a reduction in CNR by 70% with severe image
artifacts for a strong aberrator. PAC slightly lowered CNR for no aberrator, but improved CNR
by 31.2% for a weak aberrator and 134.6% for a strong aberrator. The combined method
outperformed both PAC and DAX for all three cases yielding CNR values of 10.30 for no
aberrator, 10.21 for a weak aberrator, and 10.74 for a strong aberrator.
32

Fig. 2-10. Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with no aberrator.

Fig. 2-11. Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 25ns RMS 5mm FWHM
aberrator.

33

Fig. 2-12. Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 45 ns RMS 3mm FWHM
aberrator.

2.3.2.2 Pork Tissues as Physical Aberrators

Figs 2-13 and 2-14 show the experimental images of the ATS tissue-mimicking phantom
containing anechoic cysts acquired with 4 mm and 10 mm pork tissue samples as weak and
strong physical aberrators, respectively. All images are shown on a 50 dB dynamic range. The
CNR values were calculated and summarized in Table 2-3. The CNR values for the standard
DAS beamforming decreased from 5.36 to 3.74 for 4 mm and to 1.27 for 10 mm pork tissues.
DAX increased the CNR value to 8.97 for 4 mm, but only to 1.44 for 10 mm pork. PAC, on the
other hand, increased the CNR values to 5.03 for 4 mm and to 2.99 for 10 mm pork tissues. The
estimated phase aberrator profiles for the four center image lines of both data sets are shown in
Fig. 2-15 for illustrative purposes. Lastly, the combined method further increased the CNR
34

values to 9.72 for the weak aberrator and 8.17 for the strong aberrator with high lesion visibility
for both cases.

Fig. 2-13. Experimental cysts for standard DAS beamfomring with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 4 mm pork tissue sample.

Fig. 2-14. Experimental cysts for standard DAS beamforming with uniform apodization, PAC,
DAX, and combined PAC and DAX for data sets acquired with a 10 mm pork tissue sample.

35

Fig. 2-15. Estimated aberrator profiles for a) 4 mm pork and b) 10 mm pork tissue samples.

TABLE 2-3. CNR Values for Simulation and Experimental Data

CNR values for simulated and experimental anechoic cysts with electronic and pork aberrators are
shown for standard DAS beamforming, DAX, PAC, and combined DAX and PAC. For both
simulation and experiment, results with no aberrator serve as a control for comparison.
36

2.4 Discussion
-6dB Beamwidth and First Sidelobe Level
Table 2-2 summarizes and compares the effects of weak and strong aberrators on -6 dB
beamwidth as well as the first sidelobe level. It shows that the -6 dB beamwidth in the presence
of a weak aberrator was similar to that with no aberrator. However, a greater amount of mainlobe
broadening was observed with an increase in -6 dB beamwidth from 0.45 mm to 2.13 mm in the
presence of a strong aberrator. The smallest -6 dB beamwidth of 0.48 mm was achieved by the
combined method. However, the majority of the improvements in -6 dB beamwidth obtained by
the combined method was contributed by PAC. This shows that DAX, which could only produce
an improvement in -6 dB beamwidth to 1.93 mm, gained large benefits from using PAC.
The advantage of integrating DAX and PAC is not fully apparent until its effect on the
sidelobe level is compared with those for DAX alone and PAC alone. In Table 2-2, DAX did not
suppress the first sidelobes, which was raised to –8.6 dB and 0 dB in the presence of weak and
strong aberrations. PAC, however, successfully lowered them by 19.8 dB and 29.6 dB for the
two cases. In the case of a weak aberration, the majority of the sidelobe suppression of 29.9 dB
achieved by the combined method still comes from PAC. But, DAX combined with PAC had an
additional 10.1 dB of suppression. With a strong aberration, a greater contribution of PAC was
observed with a sidelobe suppression of nearly 30 dB, which helped gain additional suppression
of 13.1 dB with DAX. Therefore, the synergistic enhancement becomes more pronounced with
increased aberration strengths. Moreover, when an aberrator is present, the performance of the
combined method in terms of improvements in –6 dB beamwidth and the amount of sidelobe
37

suppression was always superior than those of the standard DAS beamforming, DAX alone, and
PAC alone.

Anechoic Cyst Simulations
The results summarized in Table 2-3 show that the results with DAX were always better
than those with PAC except when a strong aberrator is present. DAX performed in a highly
robust manner and increased the CNR from 5.21 to 10.70 with no aberrator and from 4.10 to
8.50 with a weak aberrator. Since these CNR values are already far greater than that of an
unaberrated cyst with standard DAS beamforming, additional CNR improvement accomplished
by integrating the two methods in these cases is not of major importance. Also, the images were
free of artifacts as shown in Figs 2-7 and 2-8. However, in the presence of a strong aberrator, the
performance of DAX diminished as shown by a reduced improvement in CNR, and resulted in
an irregularly shaped cyst as well as artifacts in the form of black spots near the cyst. PAC was
able to avoid such undesirable artifacts and enhance lesion visibility with CNR increased to 4.67.
But neither DAX alone nor PAC alone was able to achieve a CNR value above that of an
unaberrated cyst with standard DAS beamforming. The limitations of the two methods were
overcome and synergistic enhancement of image contrast without any artifacts was observed
when the combined method was used. The CNR was increased to 9.80, which is greater than
those obtained with DAX alone and PAC alone. This is in good agreement with the results for
point target simulations, which showed that the combined method was most beneficial in
suppressing sidelobes and clutter with increased aberration strength.

38

Experimental Data with Electronic Aberrators
The results from electronically aberrated experimental data sets were consistent with the
trends shown by the point target and anechoic cyst simulations. The combined method yielded
CNR values of 10.30, 10.21, and 10.74 for the three aberration strengths, which were comparable
to the simulation results. The increased CNR values were further verified by the speckle
brightness improvements of 40.3% and 94.2% at the transmit focus for the weak and strong
aberrations. The irregular shape and black artifacts as a result of applying DAX on a simulated
cyst with a strong aberrator shown in Fig. 2-9 was reproduced with experimental data with the
same aberrator applied electronically. The shape and amount of artifacts found in the
experiments may vary from those in simulation mainly due to the random nature of speckle. In
the absence of aberration, PAC resulted in a CNR value of 4.97, which is slightly lower than a
CNR of 5.36 with DAS beamforming. This is expected and is associated with the jitter error,
which places a fundamental limit on the performance of the delay estimation algorithm based on
the array element uniformity, channel SNR, the segment length, and the size and strength of the
aberration across the array (Fernandez, 2002). However, the combined method still guarantees a
significant improvement in CNR since the standard deviation of the jitter error was measured to
be only 8.3 ns and induces negligible effect on image contrast.

Experimental Data with Pork Aberrators
Since physical aberrators are more reflective of clinical scenarios than electronic
aberrators, which do not account for signal attenuation and distortion that may occur with body
tissues, evaluation of the performance of DAX, PAC, and the combined method using pork
39

tissues as physical aberrators is important especially for human in-vivo studies in the future. The
results with pork aberrators shown in Figs 2-13 and 2-14 were in good agreement with the
simulation and electronic aberrator studies. The CNR values for all methods were comparable to
those obtained for the simulation and electronic aberrator studies. A more coherent summation of
the waves as a result of phase correction was also confirmed by speckle brightness improvements
of 27% and 58% for pork tissues of thickness 4 mm and 10 mm. Again, the anechoic cyst, which
was completely masked by the effects of 10 mm-thick pork aberrator, was clearly visible when
the combined method was applied while DAX alone and PAC alone failed. These results confirm
the synergistic enhancements of image contrast predicted by the simulation and electronic
aberrator studies. Particularly, the results consistently showed and confirmed that the combined
method is most useful and achieves the greatest amount of contrast enhancement when a strong
aberrator is present.
Considering the fact that DAX alone had a tendency to create image artifacts and the
contrast enhancements achieved by either DAX alone or PAC alone, if any, were not sufficient
in the presence of a strong aberrator, the achievement of the proposed method is very compelling
and shows strong potentials for enhanced visualization of anechoic regions. On the other hand, it
is important to recognize that DAX is limited in its utility to clinical applications which do not
involve multiple contrast levels. For example, visualization of hypoechoic and hyperechoic
lesions in the breast, liver, and prostate may not be enhanced by DAX in its current form. Thus,
some of the immediate clinical imaging applications ideally suited for the proposed method
would include delineation of endocardial borders and differentiation between solid and cystic
masses in breast imaging (Basset et al, 1997), visualization of cystic liver lesions and dilated bile
40

ducts in hepatic imaging (Semelk, 2005), and imaging of gallbladder stones and polyps,
assessment of thrombus or plaque in the abdominal aorta, solid organ and transplant vasculature
in abdominal imaging.
2.5 Summary and Conclusion
This paper has evaluated and compared the performance of DAX, PAC, and combined
DAX and PAC in terms of CNR improvement in the presence of different levels of aberration.
The results presented in this study confirmed the findings reported previously (Seo and Yen,
2009) that DAX is capable of reducing sidelobes and clutter and achieves a 139.8%
improvement in CNR compared with standard DAS beamforming in the presence of weak
aberration from 4 mm pork, but improves CNR by only 13.3% and can cause artifacts in the
presence of strong aberration with 10 mm pork. This is due to the fact that the sidelobes are
raised to a level where DAX is unable to make distinctions between the mainlobe-dominated
signals and the side-lobe-dominated signals. In this paper, it has shown that this problem could
be overcome by integrating it with an NNCC-based PAC algorithm, which is effective in
lowering high sidelobes. The improvements in cyst contrast as well as the visualization of the
lesion boundaries using the proposed method were presented in this work.
In conclusion, this paper has demonstrated that phase correction combined with DAX is
an effective way to improve image contrast. The results shown in this work suggest that just a
single iteration of phase correction combined with DAX can achieve improvements of 543% in
image contrast even in the presence of a strong aberrator. Furthermore, DAX is computationally
41

inexpensive because calculation of cross-correlation coefficients only at zero-lag on a 23-sample
segment of RF data at 45MHz sampling frequency is necessary.

42

Chapter 3 Effects of Dual Apodization with Cross-
correlation on Tissue Harmonic and Pulse Inversion
Harmonic Imaging in the Presence of Phase Aberration

3.1 Introduction
3.1.1 Background
Diagnostic ultrasound has experienced a great number of technological advances over
past couple of decades in attempts to detect and display new information and to pursue
improvements in accuracy of the information being presented. Among the many such
developments, tissue harmonic imaging (THI), first introduced by Averkiou et al in 1997
(Averkiou et al, 1997), as a result of investigating the characteristics of nonlinear wave fields, is
considered one of the more notable improvements that have had an impact on the medical
ultrasound community. Today, THI is widely used in clinics and has been proven useful in
detecting subtle lesions in organs such as the thyroid and breast, delineating endocardial borders
and visualization of cardiac chambers, as well as in abdominal imaging (Kornbluth, 1998;
Shapiro et al, 1998; Szopinski et al, 2003a; Szopinski et al, 2003b).
43

THI is distinct from conventional ultrasound imaging in that it utilizes nonlinear acoustic
wave propagation within the body to generate an ultrasound image. In contrast to linear acoustics,
which assumes constant speed of wave propagation, nonlinear acoustics describes the speed of
wave propagation, c as a function of the particle velocity u, which varies over the propagation
path z (Hamilton and Blackstock, 1998):

𝑐 𝑧 = 𝑐
!
+ (1+
𝐵
2𝐴
)𝑢(𝑧) (3.1)

where c
o
is the average acoustic velocity in the medium, (1+B/2A) is the coefficient of
nonlinearity of the medium, u(z) is the particle velocity at a point z along the propagation path,
and c(z) is the acoustic velocity at that point. Since a sound wave is a pressure wave that
compresses and relaxes the tissue as it travels through the body, the particle velocity u(z)
becomes positive during the compressional phase, and thus, increases the sound speed c(z).
Similarly, the particle velocity becomes negative during the rarefaction phase, resulting in a
decrease in sound speed. Such a variation in sound speed leads to a distortion in the shape of the
transmitted sinusoidal waveform to a sawtooth-like wave, which becomes more pronounced as
the wave travels through the body. When the sinusoidal waveform undergoes such a distortion
as it travels though the body, some of the energy at the fundamental frequency shift into
harmonic frequencies that accumulate and intensify as greater distortion is experienced.
44

3.1.2 Tissue and Pulse Inversion Harmonic Imaging
The simplest and most common method used in THI to extract harmonic content from a
received echo is harmonic band filtering (Averkiou et al, 1997; Christopher, 1997; Ward et al,
1997), in which the received signal is band-pass filtered with a center frequency equal to the
second harmonic. However, this method may not completely separate the harmonic band from
fundamental band since the overlap between the two bands is inevitable, especially when a
broadband pulse is used for better axial resolution. It is possible to avoid or reduce the amount of
this overlap by generating a narrower transmit bandwidth, but at the expense of reduced axial
resolution.
One possible solution to minimize such an overlap between the fundamental and
harmonic bands is to control the spectral contents of the transmit pulse by using a highly band-
limited waveform such as a Gaussian pulse. However, it is relatively sophisticated to generate
such a signal, as a digital waveform buffer and a digital-to-analog converter are typically needed.
(Shen et al, 2005). Another attempt to overcome the limitations of harmonic band filtering is the
use of pulse inversion harmonic imaging (PIHI), which was first introduced in 1997 (Chapman
and Lazenby, 1997) and has been widely studied for its clinical benefits. This method requires
two transmit pulses along the same propagation path, one of which is shifted 180
o
out of phase
with respect to the other. The echoes from the two transmit firings are then summed to obtain a
beam with a cancellation of signals at the fundamental frequency. Hence, with the pulse
inversion technique, it is possible to efficiently remove the spectral overlap while maintaining a
45

wide bandwidth of the transmit pulse and form harmonic images without sacrificing the axial
resolution.
Both THI and PIHI utilize nonlinear distortion of the transmitted frequencies within the
body to generate an ultrasound image that is sharper and higher in contrast than the conventional
B-mode image. This is primarily due to the fact that the ultrasound beam formed using second
harmonic signal has reduced beamwidth, which leads to improved resolution (Starritt et al, 1986).
Moreover, sidelobes, grating lobes, and clutter, which may be prominent at the fundamental
frequency, are suppressed in tissue harmonic and pulse inversion harmonic images (Desser and
Jeffrey, 2001). Reverberation artifacts, which can also create image clutter, are also reduced in
THI and PIHI as the harmonic content of reverberation echoes is significantly lower when
compared to signals at the fundamental frequency (Averkiou, 2000). Lastly, since the harmonic
signals only have to pass through the aberrating layers once on receive as opposed to twice for
fundamental signals, the effects of aberration on harmonic beam are reduced as well (Desser and
Jeffrey, 2001).
Despite numerous benefits that THI and PIHI offer, they may not provide sufficient
contrast enhancement in many clinical situations, especially those that involve large patients who
pose technical challenges. Superharmonic imaging (SHI), which is a more recent technique that
takes advantage of higher harmonic signals (Bouakaz and de Jong, 2003), could be used to
further improve image contrast. However, fabrication of the transducer array capable of SHI is
much more demanding as it needs to be highly sensitive over a wide frequency range from the
transmit frequency up to its third, fourth, or even fifth harmonic (Neer et al, 2010). Therefore, a
novel technique that is designed and optimized for improving the quality of tissue and pulse
46

inversion harmonic images would be a valuable tool to fully benefit from the useful information
provided by second harmonic signals and help physicians and radiologists make diagnosis more
accurately.
3.1.3 Dual Apodization with Cross-correlation
As introduced in previous chapters of this document, Dual Apodization with Cross-
correlation (DAX) is a relatively new technique that can effectively enhance ultrasound image
contrast by suppressing side lobes and clutter (Seo and Yen, 2008a). Despite the promising
improvements DAX has demonstrated, its performance was shown to decrease, often with
undesirable image artifacts as the aberration strength was increased (Seo and Yen, 2009; Shin
and Yen, 2011; Shin and Yen, 2012). This suggests that DAX could potentially lead to
misdiagnosis if implemented on clinical ultrasound imaging systems to visualize large patients
with thick layers of subcutaneous fat that defocus the ultrasound beam and mask the signals from
structures located deep within the body.
One approach to remedy this problem is to apply DAX on tissue or pulse inversion
harmonic signals. Since the undesirable effects of aberration are greatly suppressed at the second
harmonic, a better performance of DAX is expected without creating any artifacts. This
anticipated improvement in the performance of DAX is not necessarily due to possible higher
correlation between the two harmonic RF signals with different receive apodizations. Rather, the
novelty of this approach is in using the two independent contrast enhancement mechanisms
employed by harmonic imaging and DAX that work together synergistically in minimizing the
47

effects of aberration, sidelobes, and clutter. In addition, since harmonic imaging is often
preferred over conventional fundamental imaging and has been established as the standard mode
for many clinical imaging applications (Thomas et al, 1998; Varslot et al, 2007), performance
evaluation of DAX on THI and PIHI is doubly important. Similar investigations have been made
previously by Fedewa et al (Fedewa et al, 2003), who demonstrated transmit apodizations that
generate a greater spatial coherence of the backscatter at the second harmonic than at the
fundamental. More recently, Dahl et al (Dahl et al, 2012) introduced and evaluated the
performance of a harmonic version of the short-lag spatial coherence (SLSC) imaging technique,
which relies on lateral spatial coherence of the backscatter to enhance image contrast (Dahl et al,
2011). This chapter reports findings on the performance of DAX when applied to harmonic
images and demonstrate potential clinical benefits from their complementary contrast
enhancement mechanisms.
3.2 Methods
3.2.1 Experiments in Tissue Mimicking Phantoms
For the experimental setup, radio frequency (RF) data sets were acquired from an ATS
ultrasound phantom (ATS laboratories, Bridgeport, CT, Model 549) containing 6 mm-diameter
anechoic cysts located at 50 mm in depth and sampled at 45 MHz for offline processing. This
serves as the control data set for comparison. To mimic near-field aberrating layers composed of
skin, muscle, and fat, tissues of thickness 5 mm and 12 mm from pork belly were placed in
48

between the transducer and the ATS cylindrical lesion phantom. These RF signals were collected
using a Verasonics data acquisition system (Verasonics, Redmond, WA) with a 128–element C4-
2 curvilinear array with a pitch of 409 µm. A 2-cycle transmit pulse with a center frequency of
1.96 MHz and a sub-aperture size of 64 elements were used. The parameters for the C4-2
curvilinear array used in this study are summarized in Table 3-1.

Table 3-1. Parameters for C4-2 Curvilinear Array

To compare PIHI with conventional imaging and THI, data were collected again with a
transmit pulse of same amplitude but inverted and summed together to generate a new data set
containing PI harmonic signals. For each acquisition, data from each channel were collected 12
times and averaged to minimize the effects of electronic noise. All individual channel RF signals
were band-pass filtered using a 128-tap finite impulse response (FIR) band-pass filter with
fractional bandwidth of 50 % for fundamental and 30 % for tissue harmonic and pulse inversion
harmonic data sets. Offline beamforming was then performed using Matlab (The MathWorks,
Inc. Natick, MA) with a constant f-number of 2. For the control data set, the transmit focus was
always set to a depth of 50 mm where the 6 mm-diameter anechoic cyst is located, but when a
pork tissue was used to create aberration effects, the transmit focus was shifted down by the
thickness of the pork tissue such that the beam was still focused at the depth where the 6 mm-
49

diameter cyst is located. Dynamic receive focusing was used with focal updates every 1 mm in
range. The experimental imaging parameters are summarized in Table 3-2.

Table 3-2. Parameters for Experimental Setup

3.2.2 Data Processing
Fig. 3-1 describes the process of generating various kinds of images that are presented in
this study to investigate the effects of DAX on tissue harmonic and PI harmonic imaging. The
conventional B-mode ultrasound image (Fig. 3-1e) was formed by first band-pass filtering the
time-delayed RF data (Fig. 3-1a and 3.1b) at the fundamental frequency, f
o
, summing them
across the elements (Fig. 3-1c), and then performing envelop detection using Hilbert transform
and log compression (Fig. 3-1d). The tissue harmonic image (Fig. 3-1e) was formed from the
same RF data in exactly the same manner, except the RF data was band-pass filtered at the
second harmonic, 2f
o
. The PI harmonic image (Fig. 3-1e) is also generated from second
harmonic signals, but the RF data is added to another set of RF data that has been acquired with
50

an inverted transmit pulse prior to band-pass filtering at the second harmonic (Fig. 3-1a and 3-
1b). To investigate the effects of DAX on these imaging modes (Fig. 3-1g), DAX was applied to
channel RF data after band-pass filtering (Fig. 3-1f). For all results, receive apodizations with a
10-10 alternating pattern similar in terms of wavelengths to those reported in previous studies
(Seo and Yen, 2009; Shin and Yen, 2011; Shin and Yen, 2012) were utilized as they were shown
to achieve the best performance in terms of CNR improvement without creating undesirable
black artifacts near the transmit focus. The 10-10 alternating pattern consists of a set of two
complementary apodization functions with 10 alternating elements enabled on one but disabled
on the other as shown in Fig. 3-2. Use of such apodization functions on the receive aperture
creates grating lobes that are 180 degrees out of phase with respect to one another such that the
mainlobe-dominated signals can be distinguished from clutter signals by means of normalized
cross-correlation.

Fig. 3-1. The process of forming conventional, tissue harmonic, and pulse inversion
harmonic images with and without DAX.

51

Fig. 3-2. The 10-10 alternating apodization functions used in DAX.

A segment size of 2.5 wavelengths was empirically chosen for zero-lag, normalized
cross-correlation (NCC) between the two beamformed RF signals obtained with the two
complementary receive apodization functions. By cross-correlating beamformed RF signals from
the two different RX apodizations at zero lag at every axial sample location within the FOV
followed by a thresholding operator, a weighting matrix composed of cross-correlation
coefficients ranging from the threshold value 𝜀=0.001 to 1 was created. If the coefficient is
greater than or equal to the threshold value 𝜀=0.001, the coefficient is kept, but if the coefficient
is smaller than the threshold value 𝜀=0.001, it is set to 0.001 in order to obtain 20log
10
(0.001) = -
60 dB reduction in the amplitude. Since mainlobe-dominated signals, such as those coming from
speckles, are highly correlated, coefficients associated with these signals are close to 1.
Uncorrelated clutter signals, such as those associated with cystic lesions, have coefficients close
to the threshold value of 0.001, which are multiplied to the signals to suppress them. To
minimize any artifacts due to the random nature of speckle, the weighting matrix was median
filtered. In general, smaller segment and median filter sizes tend to yield artifacts due to the
52

random nature of speckle while larger sizes have a tendency to obscure the boundaries of the
anechoic cyst and make the cyst look smaller than its actual size. After investigating the
performance of several segment and filter sizes, a segment size of 2.5𝜆 and a median filter size
of 2𝜆 × 4𝜆 have been found to yield optimal results in terms of % CNR improvement and lesion
detectability. By multiplying the resulting weighting matrix by the combined RF data, DAX
achieves a dramatic improvement in image contrast by attenuating signals dominated by clutter.
Image contrast was assessed for fundamental, tissue harmonic, pulse inversion harmonic imaging
each with and without DAX applied using the equation for contrast-to-noise ratio (CNR)
(Krishnan et al, 1997):

𝐶𝑁𝑅=
𝑆
!
− 𝑆
!
𝜎
!
(3.2)

where 𝑆
!
is the mean of the target, 𝑆
!
is the mean of the background and 𝜎
!
is the standard
deviation of the background of the envelop-detected, log compressed image in dB.

53

3.3 Results
3.3.1 Experimental Results with Pork Aberrators
Fig. 3-3 shows experimental images of a 6 mm-diameter anechoic cyst from the ATS
tissue-mimicking phantom with no aberrator using conventional, THI, PIHI with and without
DAX. Similar sets of images of the same anechoic cyst in the phantom acquired with 5 mm and
12 mm pork tissues are shown in Figs. 3-4 and 3-5, respectively. All images are shown on a 50
dB dynamic range. The CNR values were calculated and shown in Table 3-3. The CNR values
for conventional imaging at the fundamental frequency decreased from 5.32 with no aberrator to
3.42 for 5 mm, and to 0.94 for 12 mm pork tissues. DAX increased the CNR value to 9.15 for no
aberrator, 4.75 for 5 mm pork tissue, and 1.84 for 12 mm pork tissue. Similarly, the CNR values
for tissue and pulse inversion harmonic images with no aberrator were 6.35 and 7.05,
respectively and were each reduced to 6.30 and 6.31 with a 5 mm pork aberrator. Further
degradation in image quality was observed with a 12 mm pork aberrator as these CNR values
were each lowered to 3.84 and 4.31. Following the application of DAX, a considerable amount
of improvement in CNR was observed with tissue and pulse inversion harmonic images. DAX
with tissue harmonic imaging successfully suppressed the effects of aberration and achieved
synergistic enhancements of image contrast through their complementary contrast enhancement
mechanisms, yielding a CNR of 13.10 with no aberrator, 11.32 with a 5 mm pork and 7.55 with a
12 mm pork. The performance of DAX was even better with pulse inversion harmonic imaging,
showing a CNR of 16.18 with no aberrator 11.57 with a 5 mm pork and 9.31 with a 12 mm pork.
54

Fig. 3-3. Experimental cysts for conventional imaging at fundamental frequency, tissue
harmonic imaging, and pulse inversion harmonic imaging with (bottom row) and without
(top row) DAX with no pork aberrator.

Fig. 3-4. Experimental cysts for conventional imaging at fundamental frequency, tissue
harmonic imaging, and pulse inversion harmonic imaging with (bottom row) and without
(top row) DAX in the presence of a 5 mm pork aberrator.

55

Fig. 3-5. Experimental cysts for conventional imaging at fundamental frequency, tissue
harmonic imaging, and pulse inversion harmonic imaging with (bottom row) and without
(top row) DAX in the presence of a 12 mm pork aberrator.

TABLE 3-3. CNR Values for Experimental Data

CNR values for experimental anechoic cysts with pork aberrators are shown for conventional
imaging at fundamental frequency, tissue harmonic imaging, and pulse inversion harmonic imaging
with and without DAX. CNR values are shown for 5 mm (weak) and 12 mm (strong) pork
aberrations. Results with no aberrator are also shown as a control for comparison. For each of the
three cases of aberration, conventional imaging with no DAX serves as the reference value for %
CNR improvement.

56

3.4 Discussion
For different levels of aberration, the results presented in this study consistently showed
that DAX effectively increases CNR for conventional imaging, THI, and PIHI. For all % CNR
improvements presented in this study, conventional imaging with no DAX serves as the
reference. As shown in Table 3-3, the benefit of using THI or PIHI over conventional imaging in
terms of image contrast is relatively small with a CNR improvement of roughly 30 % or less.
When DAX is applied, all three imaging modes achieved notable improvements in image
contrast. Particularly, THI and PIHI both achieved CNR values above 13.
The utility of THI and PIHI becomes more apparent as a weak aberration is introduced
with a 5 mm pork tissue, which caused a 36 % decrease in CNR with conventional imaging
compared to the CNR value with no aberrator. Due to the suppression of aberration effects at the
second harmonic, THI and PIHI successfully restored some of the image contrast with CNR
improvements of 84 % and 85 %, respectively. When combined with PIHI, DAX was able to
remove most of the remaining aberration effects and achieved a CNR of 11.57, which is even
better than what was obtained with no aberration and DAX combined. DAX combined with THI
resulted in a CNR of 11.32, which is comparable to, but slightly lower than that with PIHI
because of the spectral overlap between the fundamental and the second harmonic bands that
could not be completely separated by harmonic band filtering as shown in Fig. 3-6.
For THI, band-pass filter bandwidth of 30 %, as opposed to 50 % for conventional
imaging at the fundamental frequency, was used to minimize the contributions of the spectral
overlap to the harmonic images. If larger bandwidth was chosen for the band-pass filer such that
57

the spectral overlap is not removed, it could lead to ripple-like artifacts in the tissue harmonic
images. Filter bandwidth of 30 % was also used for PIHI to be consistent with THI. The CNR
values for DAX combined with THI, and PIHI were both significantly higher than that for DAX
combined with conventional imaging, which resulted in a CNR of 4.75.

Fig. 3-6. Frequency Spectra of the received RF data for left) conventional imaging at
fundamental frequency of 1.96 MHz, center) THI, and right) PIHI at second harmonic.
The frequency response of the band-pass filter (BPF) is also shown in all 3 cases.

Finally, it is not until the strong aberration effects from a 12 mm pork tissue is
investigated that the value of using DAX combined with THI or PIHI can be fully appreciated.
Using conventional imaging at the fundamental frequency, the cyst is hardly visible with a CNR
of 0.94. In this case, DAX achieves a 96 % improvement in CNR, resulting in a CNR of 1.84.
However, the CNR is still much lower than what is needed for the cyst to be clearly visible.
Moreover, the circular shape of the cyst cannot be clearly identified and small cyst-like artifacts
are observed in the surroundings. All of these are problematic and could potentially lead to
misdiagnosis in clinics. Despite the CNR improvements of 309 % and 359 % achieved with THI
and PIHI that helped to make a meaningful contribution to enhancing lesion detectability, the
58

cyst was still masked to a certain degree by aberration effects within the cyst and the contrast
between the cyst and the background was kept below that of an unaberrated cyst. Thus, THI,
PIHI, and DAX with conventional imaging all failed to fully suppress detrimental effects of the
12 mm pork and improve image contrast without creating unwanted artifacts and cyst shape
distortions. However, DAX when combined with THI, showed a significantly greater CNR
improvement of 703 % with suppression of most of the aberration effects within the cyst. Also,
the cyst was circular in shape and free of any artifacts that were seen with conventional imaging.
With PIHI, DAX performed even better with a CNR improvement of 890 % and resulted in a
circular cyst with high lesion detectability that was free of any artifacts within and around the
cyst.
Since harmonic imaging generally suffers from low signal-to-noise ratio (SNR) because
it is based on a fraction of the transmitted pulse energy that has been converted into second
harmonic signals, it is possible that there may be adverse effects on the performance of DAX due
to low SNR of harmonic signals. Cross-correlation between two beamformed RF signals having
decreased SNR would result in a wider range of decreased cross-correlation coefficients. Hence,
DAX, in its current form, may be over-attenuating mainlobe-dominated harmonic signals at
increased depth. However, a previous study (Seo and Yen, 2009) has shown that a CNR
improvement of more than 100 % compared with conventional DAS beamforming was achieved
so long as a system SNR of 15 dB or higher was maintained. In addition, a possible solution to
avoid the undesirable over-attenuating effects of DAX due to low SNR is by applying a
weighting function as a function of depth similar to the concept of time gain compensation (TGC)
to the cross-correlation coefficient matrix.
59

3.5 Summary and Conclusion
In this work, we compared the performance of DAX with conventional imaging, THI and
PIHI in terms of CNR improvement in the presence of different levels of aberration with pork
tissues of varying thickness. The experimental results presented in this study confirmed the
findings in previous studies (Seo and Yen, 2009; Shin and Yen, 2011; Shin and Yen, 2012) that
the performance of DAX decreases with increasing aberration strength with conventional
imaging. We have shown in this work that such a limitation of DAX could be overcome when
tissue harmonic or pulse inversion harmonic imaging are used as reduced effects of aberration on
harmonic beams allow DAX to better distinguish mainlobe-dominated signals from sidelobe-
dominated signals. The improvements in cystic contrast as well as the visualization of the lesion
boundaries obtained using the proposed method were presented in this work.
In conclusion, it was demonstrated in this study that DAX with tissue or pulse inversion
harmonic imaging is an effective way to enhance ultrasound image contrast. The results in this
study show that even in the presence of a strong aberration from a 12 mm pork tissue sample,
both tissue harmonic imaging and the pulse inversion harmonic imaging greatly benefit from
DAX with CNR improvements of over 703 % and 890 % while conventional imaging only
yields 96 % with irregularly-shaped cysts with unwanted artifacts. These results suggest that
while the best performance is expected with PIHI, THI with harmonic band filtering would still
allow for a decent amount of enhancement in image contrast even in the presence of a strong
aberrator.

60

Chapter 4 Clutter Suppression Using Phase Apodization
with Cross-correlation in Ultrasound Imaging

4.1 Introduction
In medical ultrasound imaging with arrays systems, degradation of image quality due to
off-axis sidelobes and clutter inherent in conventional delay-and-sum (DAS) beamforming poses
a great challenge, particularly in the presence of various levels of phase aberration.
To enhance ultrasound image contrast, a number of different techniques has been
proposed in the past (Shankar, 1986; Forsberg et al, 2000), including some of the more recent
developments such as the general coherence factor (GCF) (Li and Li, 2000), phase coherence
factor (PCF), sign coherence factor (SCF) (Camacho et al, 2009), and short-lag spatial coherence
(SLSC) imaging (Dahl et al, 2011). GCF suppresses clutter by applying a pixel-by-pixel, target-
dependent weighting matrix computed as a ratio of the spectral energy within a low frequency
region to the total spectral energy. PCF employs an approach similar to GCF, but the weighting
matrix is computed based on phase differences of the delayed channel RF signals across the
aperture rather than coherence. SLSC, on the other hand, forms images directly using lateral
spatial coherence as the basis. Each pixel in such images is generated by computing the SLSC
value, V
SLSC
at every axial depth from the spatial coherence function and the SLSC integral.
61

Previously, a novel adaptive beamforming technique, known as Dual Apodization with
Cross-correlation (DAX), which utilizes signals coming from two distinct receive apodizations to
suppress unwanted sidelobes and clutter, was introduced (Seo and Yen, 2008a). This technique
has shown contrast improvement of 139% in simulation and 123% experimentally without
sacrificing either lateral or axial resolution (Seo and Yen, 2008a). Since DAX relies on the
quality of beam focusing, it shows limited performance in terms of contrast-to-noise ratio (CNR)
improvement and robustness to image artifacts with increased levels of phase aberration (Seo
and Yen, 2009).
In attempts to overcome such a limitation of DAX, subsequent studies have proposed
taking an integrated approach, in which DAX is combined with either phase aberration
correction based on nearest neighbor cross-correlation (Shin and Yen, 2012), tissue harmonic or
pulse-inversion harmonic imaging techniques (Shin and Yen, 2013a). These studies
demonstrated improved performance of DAX as a result of better beam focusing achieved either
by restoring the coherence of the beam by compensating for the focal error due to aberration or
by extracting only the 2
nd
harmonic signals that have reduced effects of aberration.
Despite the great promises of such combined methods, further performance enhancement
may be possible by making modifications to the DAX algorithm itself to more effectively
differentiate clutter signals from mainlobe signals. This paper proposes a new beamforming
technique called Phase Apodization with Cross-correlation (PAX), which is a modified version
of DAX, that purposely introduces phase shifts in the receive delay profiles for clutter
suppression. Although amplitude apodization has been frequently used in array-based ultrasound
imaging systems and its effects have been well investigated, an imaging technique utilizing the
62

concept of phase apodization has, to the best of my knowledge, never been introduced within the
medical ultrasound community. This paper reports the first study, which demonstrates the
potential utility of dual phase apodization for ultrasound image contrast enhancement. The goal
of this study is to show that PAX can achieve greater contrast enhancement when compared to
DAX and minimizes or removes much of the black artifacts often observed with DAX in the
presence of strong aberrators.

4.2 Theory
Motivated by the concept of thin sinusoidal phase gratings and its mathematical
formulations from optics (Goodman, 1996), a pair of complementary sinusoidal phase
apodizations, such as those shown in Fig. 4-3b, is introduced. Their effects on the pulse-echo
field can be approximated using the Rayleigh-Sommerfeld diffraction theory and the Fresnel
approximation. The transmit-receive field, 𝜓 !
as a result of DAS beamforming at frequency 𝜔 at
field point (x, z) can be expressed as:

𝜓 !
𝑥,𝑧 =
!
!"#
!"#
!
𝑎
!
𝑥
!
𝑒
!
!"#!
!
!
!
!!
𝑑𝑥
!
𝑎
!
𝑥
!
𝑒
!
!"#!
!
!
𝑒
!!!
!
!
(
!
!!
!
!
!!
!
) !
!!
𝑑𝑥
!
(4.1)

where 𝜆 is the wavelength, 𝑘 =
!𝜋 𝜆 is the wave number, 𝑧 𝐹 is the transmit focal depth, and 𝑎 !
𝑥 !

and 𝑎 !
𝑥 !
are the transmit and receive apertures with 𝑥
!
as the azimuth coordinate on the
63

aperture surface. Introduction of a sinusoidal phase apodization to the receive aperture is
equivalent to multiplying the 1
st
integrand in Equation (4.1) with 𝑒
!
!
!
!"#(!!!
!
!
!
)
, where 𝑚 is the
peak-to-peak phase delay in radians, and 𝑓
!
is the spatial frequency of the phase apodization in
cycles per meters. Hence, the transmit-receive field, 𝜓 !,!"
as a result of DAS beamforming at
frequency 𝜔 at field point (x, z) with a sinusoidal phase apodization applied to the receive
aperture can be expressed as:

𝜓
!,!"
𝑥,𝑧 =

!
!"#
!"#
!
𝑎
!
𝑥
!
𝑒
!
!"#!
!
!
𝑒
!
!
!
!"#(!!!
!
!
!
)
!
!!
𝑑𝑥
!
𝑎
!
𝑥
!
𝑒
!
!"#!
!
!
𝑒
!!!
!
!
(
!
!!
!
!
!!
!
) !
!!
𝑑𝑥
!
(4.2)

At the transmit focal depth 𝑧 = 𝑧
!
, the quadratic phase factor is cancelled and the complex
transmit field becomes 𝐴 !
𝑢 𝑥 =ℱ 𝑎
!
(𝑥
!
)
𝑢 𝑥 !
𝑥 𝜆𝑧
, and hence, the pulse-echo field can be
described as:

𝜓
!,!"
𝑥,𝑧 =
!
!"#
!"#
!
𝐴
!
(𝑢
!
) 𝑎
!
𝑥
!
𝑒
!
!"#!
!
!
𝑒
!
!
!
!"#(!!!
!
!
!
)
!
!!
𝑑𝑥
!
(4.3)

The analysis can be further simplified by use of the identity:

𝑒
!
!
!
!"#(!!!
!
!
!
)
= 𝐽
!
!
!!!!
!
!
𝑒
!!!"!
!
!
!
(4.4)

64

where 𝐽
!
is the Bessel function of the first kind and of order q (Goodman, 1996). Hence, the
equation becomes:

𝜓
!,!"
𝑥,𝑧 =
𝑒
!"#
𝑗𝜆𝑧
!
𝐴
!
(𝑢
!
) 𝐽
!
!
!!!!
𝑚
2
𝑎
!
𝑥
!
𝑒
!
!!!!!
!
!"
𝑒
!!!!"
!
!
!
!
!!
𝑑𝑥
!

=
!
!"#
!"#
!
𝐴
!
(𝑢
!
) 𝐽
!
!
!!!!
!
!
𝐴
!
(𝑢
!
−𝑞𝑓
!
) (4.5)

If both the transmit and receive apertures are 1-D arrays of finite length 2a, the above equation
becomes:

𝜓
!,!"
𝑥,𝑧 =
𝑒
!"!
𝑗𝜆𝑧
!
2𝑎
!
𝑠𝑖𝑛𝑐 2𝜋𝑎 𝑢
!
𝐽
!
!
!!!!
𝑚
2
𝑠𝑖𝑛𝑐 2𝜋𝑎 𝑢
!
−𝑞𝑓
!

=
!
!"#
!"#
!
2𝑎
!
𝑠𝑖𝑛𝑐 2𝜋𝑎
!
!"
𝐽
!
!
!!!!
!
!
𝑠𝑖𝑛𝑐
!!"
!"
𝑥−𝑞𝑓
!
𝜆𝑧 (4.6)

The equation (4.6) obtained from Rayleigh-Sommerfeld analysis predicts that the sinusoidal
phase apodization on the receive aperture deflects the main beam energy into multiple grating
lobes characterized by the Bessel function 𝐽
!
of the first kind. The grating lobes are located at a
distance of ±𝑞𝑓
!
𝜆𝑧 from the center. Manipulation of this formulation and carefully selecting the
parameters associated with it allow for more flexibility in manipulating the locations and the
magnitudes of the grating lobes in a controlled manner. Thus, this will help guide the design of
65

phase apodizations that are more robust and effective in creating phase diversities in the clutter
signals, which can then be detected by the use of zero-lag normalized cross-correlation.

4.3 Methods
4.3.1 Simulation Experiments in Field II
To assess and compare the performance of PAX with that of DAX as well as
conventional DAS beamforming, point target and anechoic cyst simulations were performed
using Field II with imaging parameters chosen to model a 128-element linear array with center
frequency of 5MHz, 50% bandwidth, and an azimuthal element pitch of 308 um as summarized
in Table 4-1. For anechoic cyst simulations, channel RF signals from a 3 mm diameter anechoic
cyst at a depth of 30 mm away from the transducer face were generated.

TABLE 4-1. Field II Simulation Parameters

66

For both point target and anechoic cyst simulations, zero-mean, random electronic near-
field phase screens were generated by convolving Gaussian random numbers with a Gaussian
function (Dahl et al, 2005) to mimic aberrating layers on the beam. Weak (25ns RMS 5mm
FWHM) and strong (45ns RMS 3mm FWHM) aberrator profiles were created as shown in Fig.
4-1, and applied on both transmit and receive during simulation.

Fig. 4-1. Aberrator profiles of 25 ns RMS 5mm FWHM (dashed line) and 45 ns RMS 3mm FWHM
(solid line).

4.3.2 DAX and PAX Processing
For all simulations performed in this study, a set of two complementary square wave
functions with an 8-8 alternating pattern was used for DAX as reported in a previous study (Shin
and Yen, 2012). Similarly, for PAX, a set of two complementary sinusoidal functions with 𝑘𝑚 =
2𝜋 and 𝑓
!
= 420 cycles/meter was used to introduce time delays in the channel RF data prior to
summing. A PAX system diagram is shown in Fig. 4-2 and the apodizations used for DAX and
PAX are shown in Fig. 4-3.
67

Fig. 4-2. A system diagram for PAX

Fig. 4-3. a) Amplitude and b) phase apodization functions used in DAX and PAX,
respectively.

b)
a)
68

With two beamformed RF data obtained from the two distinct apodizations - either
amptliude-based or phase-based - a segment length of 2.2 wavelengths was selected for zero-lag
cross-correlation between them to create a weighting matrix filled with normalized cross-
correlation coefficients ranging from 0 to 1 after thresholding at 0.001. In order to minimize the
artifacts in the form of black spots which may arise due to the random nature of speckle, the
weighting matrix was median filtered with a window size of 2𝜆 × 4𝜆. Improvements in image
contrast achieved by DAS beamforming, DAX, and PAX were compared for no, weak, and
strong aberrators. Performance was evaluated using the CNR equation:

𝐶𝑁𝑅=
𝑆
!
− 𝑆
!
𝜎
!
(4.7)

where 𝑆
!
is the mean of the target, 𝑆
!
is the mean of the background and 𝜎
!
is the standard
deviation of the background of the envelop-detected, log-compressed image.

4.3.3 Experiments with Tissue Mimicking Phantoms
To validate the results from Field II simulations, imaging experiments were performed as
described in (Shin and Yen, 2012). Full synthetic aperture radio frequency (RF) data sets were
acquired from an ATS ultrasound phantom (ATS laboratories, Bridgeport, CT, Model 549)
containing 3 mm-diameter anechoic cysts located at 30 mm in depth. Pork tissue samples of
69

thickness 4 mm and 10 mm composed of skin, muscle, and fat were used to mimic near-field
aberrating layers. These RF signals were collected using a Verasonics data acquisition system
(Verasonics, Redmond, WA) at 45 MHz sampling frequency with a 128–element, 298 µm pitch
a L7-4 linear array. A 1-cycle transmit pulse with a center frequency of 5 MHz and a subaperture
size of 64 elements were used. Data from each channel were collected 12 times and averaged to
minimize the effects of electronic noise. All individual channel RF signals were band-pass
filtered using a 64-tap finite impulse response (FIR) band-pass filter with frequency range
limited to the -6 dB bandwidth of the transducer. Offline DAS beamforming was then performed
using Matlab (The MathWorks, Inc. Natick, MA) with a constant f-number of 2. The transmit
focus was set to a depth of 30 mm when no aberrator was used, but it was moved down by the
thickness of the pork tissue when it is introduced. Focal updates every 1 mm in range and an
image line spacing of 100 µm were used for dynamic receive focusing. DAX and PAX were also
performed and their performance was compared with DAS beamforming in terms of CNR
improvement as done for simulation study described above.

70

4.4 Results and Discussion
4.4.1 Point Target Simulations
Fig. 4-4 shows simulated lateral beamplots for DAS, DAX, and PAX with varying levels
of phase aberration. In all cases, DAX and PAX resulted in similar beamplots with comparable
first sidelobe level and -6dB beamwidth. Fig. 4-4a compares the beams created using
complementary phase apodizations (red and blue) with standard DAS beamforming. The first
grating lobes are present at ±4.5 mm, which agrees with equation (4.6). After performing PAX
processing, a beam very similar to DAX is seen in Fig. 4-4b. When applying a weak aberrator,
the performance of DAX and PAX are similar as shown in Fig. 4-4c. For the strong aberrator
(Fig. 4-4d), DAX tends to produce a beam with abrupt discontinuities near the high sidelobes,
which are not observed with DAS. PAX tends to produce a beam that is quite similar to, but
lacks the abrupt discontinuities seen with DAX. From the beamplots alone, one cannot predict
how PAX will perform when imaging speckle-generating targets.

71

Fig. 4-4. a) Simulated lateral beamplots using complementary phase apodization (red and
blue) compared with DAS (black). Simulated lateral beamplots are shown for DAS (black),
DAX (blue) and PAX (red) with b) no aberrator, c) a weak (25ns RMS 5mm FWHM)
aberrator, and d) a strong (45ns RMS 3mm FWHM) aberrator.

b) a)
c) d)
72

4.4.2 Simulated and Experimental Anechoic Cysts
Figs. 4-5 and 4-6 show simulated and experimental anechoic cysts, respectively, for DAS,
DAX, and PAX with varying levels of phase aberration. The performance of PAX is compared
with that of DAS and DAX, which have been published previously (Shin and Yen, 2012).

Fig. 4-5. Simulated cysts for conventional DAS beamforming, DAX, and PAX in the
presence of top) no aberrator, middle) a weak (25ns 5mm FWHM) aberrator, and bottom)
a strong 45ns RMS 3mm FWHM) aberrator.

73

Fig. 4-6. Experimental cysts for conventional DAS beamforming, DAX, and PAX in the
presence of top) no aberrator, middle) a weak (4 mm pork) aberrator, and bottom) a
strong (10 mm pork) aberrator.

The CNR values are summarized in Table 4-2. The simulation and experimental results are in
good agreement in terms of CNR and overall image quality. In cases of no aberrator and a weak
aberrator, PAX achieved CNR improvements comparable to those of DAX, with little or no
visual difference in image contrast, target size, and shape. However, in the presence of a strong
aberrator, PAX outperforms DAX in both simulation and experiment with greater CNR
improvements and reduced image artifacts near the cyst. Hence, these results demonstrate that
PAX has potential to improve contrast with increasing levels of phase aberration.
74

TABLE 4-2. Summary of CNR Values for DAS, DAX, and PAX

4.5 Conclusions and Future Work
Both simulation and experimental results presented in this work show that PAX achieves
CNR improvements comparable to DAX with no or weak aberrator and greater CNR
improvement as well as reduction of image artifacts that DAX tends to create in the presence of
strong aberration effects. For fair comparison between DAX and PAX, the relevant parameters
were empirically selected to yield the best performance for each method. Since the performance
of PAX may vary depending on the selection of the peak-to-peak phase delay and the spatial
frequency of the phase apodization functions, future work involves further investigation for
optimal design of such phase apodization functions and validation of these results in vivo.

!

Simulation Experiment
DAS DAX PAX DAS DAX PAX
No Aberrator 5.20 10.70 10.98 5.00 12.59 12.44
Weak Aberrator 4.10 8.50 8.65 3.10 6.98 7.57
Strong Aberrator 1.69 3.17 5.28 1.75 2.31 6.13

75

Chapter 5 Multi-Apodization Techniques for Robust Reverberation
Clutter Suppression in Ultrasound Imaging

5.1 Introduction
In previous studies, two distinct families of approaches have been explored in order to
overcome the inherent limitations of DAX. First, integration of DAX with phase aberration
correction (PAC) based on nearest-neighbor cross-correlation, tissue harmonic imaging (THI) or
pulse inversion harmonic imaging (PIHI) has been proposed (Shin and Yen, 2012; Shin and Yen,
2013a). PAC aims to restore coherence by estimating and correcting for focusing errors that
cause degradation in image quality whereas THI and PIHI take advantage of the reduced
aberration effects at the second harmonic content of the received echo signals. Integration of
DAX with such imaging techniques seeks to achieve synergistic enhancements of ultrasound
image contrast from their independent contrast enhancement mechanisms. Second, a modified
version of DAX called Phase Apodization with Cross-correlation (PAX), which introduces
sinusoidal time or phase delays in the received channel RF data, was proposed (Shin and Yen,
2013b). By selecting proper values for parameters associated with the peak-to-peak excursion
and the spatial frequency of the sinusoidal time or phase delay, PAX allows for precise control of
76

both the grating lobe magnitude and location. PAX has shown CNR improvements over DAX in
both simulated cysts and tissue mimicking phantoms in the presence of varying levels of phase
aberration. It was also shown that when compared to DAX, PAX is less prone to creating image
artifacts in the case of strong aberration.
Although previous studies on DAX and PAX have shown promising results and
demonstrated that both methods are highly effective in suppressing clutter due to off-axis
sidelobes in simulation and experimental tissue mimicking phantoms, their performance would
suffer from a high level of reverberation clutter from near-field structures in in-vivo
environments. Particularly in echocardiography, reverberation clutter often obscures the
endocardial borders and thereby poses a great challenge for cardiologists to obtain accurate
measurements of mass, volume, ejection fraction and myocardial strain for assessment and
prediction of cardiac function and disease (Teske et al, 2007). A simulation study reported by
Pinton et al. has concluded that reverberation clutter is the dominant mechanism of image quality
degradation for fundamental frequency B-mode imaging (Pinton et al, 2011). Other studies have
reported that not only can clutter signals dominate over signals due to scattering from blood cells
in myocardial cavities, but also they can be stronger than the signals from myocardium itself
(Vançon et al, 2003; Giglio et al, 2002). In abdominal imaging, Lediju et al reported that clutter
can range from 0 to -35 dB relative to the surrounding tissue (Lediju et al, 2008).
Several different approaches for reverberation clutter suppression have been proposed in
the past. Harmonic imaging, which is often established as the standard mode for cardiac imaging,
is probably the most popular approach among them. It reduces near-field reverberation clutter as
its energy contribution to the 2
nd
harmonic content of the received echo is much less prominent
77

(Pinton et al, 2011). A different approach that induces axial displacement during imaging and
utilizes a set of finite impulse response and blind source separation motion filters to remove
clutter that moves with the background structure (Lediju et al, 2009). Other techniques that have
been successful in suppressing reverberation clutter include short-lag spatial coherence (SLSC)
(Dahl et al, 2011), and a model-based signal decomposition approach (Byram et al, 2014).
Since reverberation clutter likely dominates over the grating lobes generated by DAX and
PAX, these dual amplitude or phase apodization-based methods would lose effectiveness in their
performance. This is because they require that the grating lobe magnitude be dominant over the
clutter level such that the beamformed RF data from the two complementary apodizations would
exhibit clear phase differences that can be detected by means of zero-lag normalized cross-
correlation. In order to address this issue and develop a highly robust approach to clutter
suppression, this paper proposes two new techniques called Multi Apodization with Cross-
correlation (MAX) and Multi Phase Apodization with Cross-correlation (MPAX), each of which
is an extension of DAX and PAX.

78

5.2 Methods
5.2.1 Multi Apodization Schemes
5.2.1.1 Multi Apodization with Cross-correlation (MAX)
Previously DAX was described as having two complementary square wave apodizations.
For example, a 4-4 alternating pattern, in which a set of two complementary apodization
functions with 4 alternating elements are enable on one but disabled on the other, is depicted in
Fig. 5-1. Such a pair of complementary apodizations would generate two different point spread
functions having similar mainlobe signals but very different clutter patterns because of the
grating lobes introduced by the relatively large effective pitch. The differences in the clutter
patterns manifested as phase differences in the two beamformed RF data are then detected by
computing zero-lag normalized cross-correlation coefficient between them.
Since one time computation of normalized cross-correlation coefficient for each pixel in
the field-of-view (FOV) would lose effectiveness and lead to suboptimal weighting matrix when
a high level of reverberation clutter is present, this paper proposes using multiple sets of
apodization pairs in order to create more phase diversity for increased robustness in the presence
of high levels of reverberation clutter. Each of the N-N alternating apodizations for DAX
depicted in Fig. 5-1 for N = 4 as an example, can be further divided and grouped into N distinct
apodizations having the same effective pitch as shown Fig. 5-2.
79

Fig. 5-1. 4-4 Alternating DAX Apodization Functions

Fig. 5-2. MAX (N=4) Apodization Functions

80

For MAX, 2D normalized cross-correlation is adopted instead of 1D axial cross-
correlation in order to maximize its performance (Seo and Yen 2008b). Thus, MAX computes
2D normalized cross-correlation at zero-lag between every possible combination of N RX1
apodizations and N RX2 apodizations, yielding a total of N
2
coefficients for each pixel. In other
words, zero-lag 2D normalized cross-correlation coefficient is computed between RX1
i
and RX2
j

for all i and j for the l
th
sample on image line m with a 2D cross-correlation kernel size of 2A+1
samples axially and 2B+1 laterally:

𝜌 𝑙,𝑚 =
𝑅𝑋1
!
(𝑘,𝑚)𝑅𝑋2
!
(𝑘,𝑚)
!!!!!
!!!!!
!!!
!!!!!
𝑅𝑋1
!
(𝑘,𝑚)
! !!!
!!!
!!!
!!!!!
𝑅𝑋2
!
(𝑘,𝑚)
! !!!
!!!
!!!
!!!!!
𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 & 𝑗 (5.1)

While the mean of the resulting N
2
coefficients corresponding to mainlobe signals is expected to
be close to 1 with a relatively small variance, the mean of the N
2
coefficients corresponding to
signals dominated by reverberation clutter is expected to be much lower with a larger variance.
Therefore, the resulting N
2
cross-correlation coefficients associated with each pixel are sorted in
increasing order from 1 to N
2
. The L
th
smallest set of coefficients is selected for optimal
performance on the basis of contrast (C), contrast-to-noise ratio (CNR), and speckle signal-to-
noise ratio (SNR) as defined by:

𝐶= 20𝑙𝑜𝑔
!"
𝑆
!
𝑆
!
(5.2)

81

𝐶𝑁𝑅=
𝑆
!
− 𝑆
!
𝜎
!
(5.3)

𝑆𝑝𝑒𝑐𝑘𝑙𝑒 𝑆𝑁𝑅=
𝑆
!
𝑆
!
(5.4)

where 𝑆
!
is the mean of the target, 𝑆
!
is the mean of the background and 𝜎
!
is the standard
deviation of the background. CNR calculation is performed on log-compressed data while
contrast and speckle SNR calculations are performed on uncompressed data. Once the optimal L
value has been determined, a thresholding operator is applied to the L
th
smallest coefficient
matrix such that the coefficients range from the threshold vale 𝜀=0.001 to 1. Any coefficients
smaller than the threshold value 𝜀=0.001 are set to 0.001 to obtain 20log
10
(0.001) = -60 dB
reduction in the amplitude. 2D median filtering employed in DAX and PAX is no longer used in
MAX. Next, the standard DAS beamformed RF data is multiplied by the coefficient matrix so
that clutter-dominated signals are suppressed while the mainlobe-dominated signals remain intact.

5.2.1.2 Multi Phase Apodization with Cross-correlation (MPAX)
In a manner similar to DAX, PAX can also be extended to MPAX by simply varying
either or both of the peak-to-peak excursion, m and the spatial frequency of the sinusoidal phase
apodization, f
0
to generate multiple sets of 2D normalized cross-correlation coefficients. By
selecting N sets of values for these parameters for precise control of grating lobe magnitudes and
82

locations, it is possible to generate N pairs of complementary phase apodizations from which N
normalized 2D cross-correlation coefficients are obtained. The rest of the steps, including
optimization of the L value and thresholding, are identical to MAX.
The theoretical diffraction efficiency of the sinusoidal phase apodization depicted in Fig.
5-3 for mainlobe (q = 0), 1
st
grating lobe (q = 1) and 2
nd
grating lobe (q = 2) may be useful in
selecting proper m values. The 0
th
order mainlobe vanishes completely whenever m/2 is a root of
J
0
and the largest possible diffraction efficiency into one of the 1
st
order grating lobes is equal to
the maximum value of 𝐽
!
!
, which is much greater than the maximum diffraction efficiency with
amplitude apodizations (Goodman, 1996). Furthermore, since grating lobes are located at a
distance of ±𝑞𝑓
!
𝜆𝑧 from the mainlobe (Shin et al 2013b), the spatial frequency 𝑓
!
of the
sinusoidal phase apodization can be carefully selected to place the grating lobes at desired
locations. Examples of complementary sinusoidal phase apodizations are shown in Fig. 5-4 for 3
different f
0
values at m = 3.6 rad.

Fig. 5-3. Diffraction efficiency 𝑱
𝒒
𝟐
(𝒎 𝟐) vs. m/2 for three values of grating order q.
83

Fig. 5-4. Examples of complementary sinusoidal phase apodizations used in PAX and
MPAX. Sinusoidal time delays with 3 different f
0
values are shown for m=3.6 rad: top) f
0
=
342 cycles/m, middle) f
0
= 391 cycles/m, and bottom) f
0
= 635 cycles/m.

84

5.2.2 Point Target Simulation Experiments in Field II
Computer simulations for a point target were performed using Field II (Jensen, 1992) to
compare the effects of various apodization schemes used in the four processing methods: DAX,
PAX, MAX, and MPAX. Imaging parameters were chosen to model a 64-element ATL P4-2
phased array with center frequency of 2.5 MHz, 50% bandwidth, and an azimuthal element pitch
of 320 µμm as summarized in Table 5-1. For DAX, a 4-4 alternating pattern as shown in Fig. 5-1
was selected. These are equivalent to two complementary square wave apodizations having an
effective pitch of 8 × 0.320 mm = 2.56 mm. To be consistent with DAX in terms of the effective
pitch, N=4 was also selected for MAX, allowing for a total of N
2
= 16 independent 2D
normalized cross-correlation computations. For PAX, the spatial frequency of the phase
apodization, f
0
, was chosen to be 391 cycles/m so that the grating lobe locations were similar to
those of DAX and MAX. Also, m = 3.6 rad was selected to achieve grating lobe magnitudes at
least 10 dB higher than those of DAX. The corresponding phase apodizations are shown in Fig
5-4b. For MPAX, 16 different f
0
values ranging from 342 cycles/m to 635 cycles/m at an
increment of 19.5 cycles/m were selected for a fair comparison with MAX which also has total
of 16 measurements with N=4. These f
0
values were selected such that the grating lobes move
from ± 14.7 mm to ± 27.4 mm at an increment of 0.84 mm. Among the 16 phase apodization
pairs for MPAX used in this study, those with f
0
of 342 cycles/m (solid lines), 391 cycles/m
(dashed lines), and 635 cycles/m (dash-dot lines) are shown for m = 3.6 rad in Fig. 5-4.

85

TABLE 5-1. Field II Simulation Parameters

5.2.3 Experimental Data from Sponge Phantom
The performance of the four methods DAX, PAX, MAX, and MPAX were evaluated
with a custom sponge phantom (Grease Monkey Pro Cleaning Hydrophilic Sponge, Big Time
Products LLC, Rome, GA) with a 4 cm-diameter circular hole. The diameter of the hole is
intended to be comparable to the typical end-diastolic transverse diameter of the human left
ventricle (O’Connor, 2009). A previous study has reported that a highly-reflective copper wire
mesh produces clutter having similar characteristics to that of in-vivo data (Lediju et al, 2008).
The study reports that the magnitude of the clutter generated by the copper wire mesh was
comparable to that of in-vivo data with decreasing magnitude with depth. Hence, in order to
mimic near-field reverberation effects, a wiry copper household scouring pad (Practical Matter
Copper Mesh Scourers, IMS Trading LLC, Los Angeles, CA) was cut to roughly 1 cm in
thickness and placed at the surface of the transducer. Individual channel RF signals were
Parameters Value
Number of Elements in Subaperture 64
Center Frequency 2.5 MHz
Bandwidth 50%
Azimuthal Element Pitch 320 !m
Elevation Element Height 13 mm
Sound Speed 1540 m/s
Transmit Focus 70 mm
Angular Beam Spacing 0.46
o

86

acquired from the abovementioned custom sponge phantom immersed in a container filled with
de-gassed water. Data acquisition was performed using a Verasonics data acquisition system
(Verasonics, Redmond, WA) with a 64-element P4-2 phased array transducer at a rate of 15
frames/s. Total of 18 frames were acquired from a custom sponge phantom with and without a
copper wire mesh at the transducer surface. A 1-cycle pulse with a center frequency 2.5 MHz
was used and total of 128 transmit beams with a transmit focus at an axial depth of 7 cm were
used over a 72
o
field-of-view at an angular beam spacing of 0.57
o
. All RF data sets were first
sampled at a sampling frequency of 30 MHz and down-sampled to 10 MHz afterwards.
A segment length of 2𝜆 and a 2D median filter size of 2𝜆 × 2𝜆 were selected for DAX
and PAX while a 2D-kernel size of 2𝜆 × 1.3𝜆 wavelength was empirically chosen for 2D
normalized cross-correlation for MAX and MPAX. Also, L =3 was selected for best performance
in terms of CNR, contrast, and speckle SNR.

5.2.4 In-Vivo Evaluation
For in-vivo performance evaluation, RF data sets were collected using the same transmit
and acquisition settings as those described for sponge phantom imaging. In order to ensure
patient safety, transmit power for the pulse sequences was determined prior to imaging the
patients based on acoustic output measurements obtained with a HNP-0150 needle
hydrodrophone (Onda, Sunnyvale, CA) and AH-1100 amplifier, such that the mechanical index
and the spatial-peak pulse average intensity do not exceed the limits established by the Food and
87

Drug Administration (Phillips and Harris 2008). Initial performance evaluation was performed
for both abdominal imaging and echocardiography.

5.3 Results and Discussion
5.3.1 Simulated Beamplots
The simulated beamplot for DAX with 4-4 alternating pattern depicted in Fig 5-5a is
compared with the simulated beamplot for MAX (N=4) shown in Fig 5-5b. Note that all 4 pairs
of MAX apodizations generate beams having same magnitudes but different phases. Since
grating lobe locations are determined by the effective pitch 2×N×g, the 1
st
grating lobes are
located at 𝑑
!
= 𝑠𝑖𝑛
!!
!
!!"
= ±13.9
o
for both DAX and MAX. However, DAX apodizations
generate grating lobes that are at least 10 dB lower than the MAX apodizations. Also, the overall
clutter level of DAX apodizations is at least 20 dB lower than that of MAX apodizations. This is
because DAX apodizations are essentially square wave functions having a fill-factor of 0.5 that
place the 2
nd
grating lobes at the 1
st
zero in the envelope (Christensen, 1988). The two methods
achieved similar level of clutter suppression without any loss in lateral resolution. The simulated
beamplots for PAX and MPAX are also shown in Fig. 5-5c. Among the 16 pairs of MPAX
beams only those corresponding to the phase apodizations shown in Fig. 5-5 are presented for
clarity (red). Since f
0
= 391 cycles/m was also used for PAX, the beamplots resulting from f
0
=
391 cycles/m (shown with dashed lines) for MPAX are identical to the beamplots generated by
88

PAX. Beamplots for standard DAS beamforming are shown for comparison with the four
methods.

Fig. 5-5. Simulated lateral beamplots for a) 4-4 DAX, b) MAX (N=4), and c) PAX and
MPAX. A beamplot for standard DAS beamforming is shown as control in all cases.
Beamplots shown in red are generated by the amplitude or phase apodizations while those
shown in blue are the final beamplots after clutter suppression. For c), PAX beams for f
0
=
342 cycles/m (solid line), 391 cycles/m (dashed line), and 635 cycles/m (dash-dot line) are
shown for m = 3.6 rad.

DAX(4-4)
a)
MAX (N=4)
b)
PAX & MPAX
c)
89

5.3.2 Sponge Phantom Results
Fig. 5-6 shows images of a 4 cm-diameter circular hole in a sponge without a copper wire
mesh at the transducer surface for standard DAS beamforming and the 4 processing methods.
Similarly, Fig. 5-7 shows images of the same target with a copper wire mesh placed at the
transducer surface. All images from Fig 5-6 and Fig. 5-7 are displayed on a 60 dB dynamic range.
Figs. 5-8 and 5-9 show the cross-correlation coefficient matrices corresponding to the 4
processing methods without and with a copper wire mesh, respectively.

Fig. 5-6. Experimental results from a custom sponge phantom without a copper wire mesh for
standard DAS beamforming and the 4 processing methods. These images serve as a control. All
images are displayed on a 60dB dynamic range.

90

Fig. 5-7. Experimental results from a custom sponge phantom with a copper wire mesh for
standard DAS beamforming and the 4 processing methods. All images are displayed on a 60dB
dynamic range.

The CNR values were calculated using equation (5.3) and are summarized in Table 5-2.
Without a copper wire mesh, The CNR value for standard DAS beamforming was 6.0 while all 4
processing methods achieved CNRs grater than 12. Both DAX and PAX were shown to be
highly effective even though further improvements were observed with MAX and MPAX. The
cross-correlation coefficient matrices in Fig 5-8 showed that all 4 methods were able to clearly
distinguish the water-filled anechoic circular target from the background speckle region. When a
near-field reverberation clutter is induced by placing a copper wire mesh at the transducer
surface, the CNR value for DAS beamforming was reduced to 2.7 and the circular anechoic
target was obscured. Although improvements were observed with both DAX and PAX with CNR
91

values of 5.4 and 6.4, respectively, their cross-correlation coefficient matrices showed that much
of the reverberation effects resulted in highly correlated signals inside the anechoic region while
they decreased signal coherence in the speckle region. However, MAX and MPAX showed
significantly more robust performance, resulting in CNR values of 9.5 and 10.3, respectively. In
all cases, CNR values for MAX and MPAX were higher than both DAX and PAX, with the latter
being the highest of all 4 processing methods.

Fig. 5-8. Final normalized cross-correlation coefficient matrices obtained without a copper wire
mesh for the 4 processing methods.

MAX Coefficient
MPAX Coefficient PAX Coefficient
DAX Coefficient
92

Fig. 5-9. Final normalized cross-correlation coefficient matrices obtained with a copper wire mesh
for the 4 processing methods.

TABLE 5-2. Summary of CNR Values from Sponge Phantom Imaging

The improvements shown by MAX, particularly in the presence of near-field
reverberation clutter can be attributed two factors: 1) larger grating lobe magnitudes associated
with smaller fill-factor of MAX apodizations, and 2) increased phase diversity from cross-
correlation between multiple independent apodization pairs. Larger grating lobe magnitudes
MAX Coefficient
MPAX Coefficient PAX Coefficient
DAX Coefficient
93

associated with MAX are important because near-field reverberation effects often dominate over
the grating lobe level, leading to an increase in signal correlation in an otherwise uncorrelated
pair of signals. In addition, since the final cross-correlation coefficient matrix is no longer
determined by a single cross-correlation calculation, but based on total of N
2
=16 coefficient
matrices between independent beamformed RF signals, each having a unique phase, any
undesirable reverberation effects in the form of increased signal correlation for some of these 16
apodization pairs are minimized or avoided.
In a manner similar to MAX, MPAX also benefits for larger grating lobe magnitudes.
However, the increase in grating lobe magnitude is due to increased diffraction efficiency
associated with sinusoidal phase apodization, rather than a smaller fill-factor in the case of MAX.
Furthermore, MPAX also benefits from increased phase diversity from multiple cross-correlation
calculations in determining a more reliable weighting matrix. However, unlike MAX, which
creates phase diversity in the beamformed RF signals by apodizing different sets of receive
channels, MPAX creates phase diversity by varying grating lobe locations.

5.3.3 In-vivo Evaluation in Echocardiography
Fig. 5-10 shows end-systolic images of an apical four-chamber view from one volunteer
for standard DAS beamforming and the 4 processing methods. Equivalent end-diastolic images
are shown in Fig. 5-11. All images are displayed on a 60 dB dynamic range.
94

Fig. 5-10. In-vivo images of an apical four-chamber view at end-systole for standard DAS
beamforming and the 4 processing methods. All images are displayed on a 60dB dynamic range.

Fig. 5-11. In-vivo images of an apical four-chamber view at end-diastole for standard DAS
beamforming and the 4 processing methods. All images are displayed on a 60dB dynamic range.
95

Figs. 5-12 and 5-13 show the cross-correlation coefficient matrices corresponding to the
4 processing methods at end-sytole and at end-diastole, respectively. Note the effects of
reverberation clutter prominent in the left and right ventricles of DAX and PAX cross-correlation
matrices are significantly improved with MAX and MPAX at both end-systole and end-diastole.

Fig. 5-12. Final normalized cross-correlation coefficient matrices of an apical four-chamber view at
end-systole for the 4 processing methods.

MAX Coefficient
MPAX Coefficient PAX Coefficient
DAX Coefficient
96

Fig. 5-13. Final normalized cross-correlation coefficient matrices of an apical four-chamber view at
end-diastole for the 4 processing methods.

An equivalent set of images of a subxiphoid view at end-systole and at end-diastole are
shown in Fig. 5-14 and Fig. 5-15, respectively, and their corresponding cross-correlation
coefficients matires are shown in Fig. 5-16 and Fig. 5-17. CNR values were calculated from the
apical four-chamber and the subxiphoid views and summarized in Table 5-3 for all processing
methods at end-systole and end-diastole.
MAX Coefficient
MPAX Coefficient PAX Coefficient
DAX Coefficient
97

Fig. 5-14. In-vivo images of a subxiphoid view at end-systole for standard DAS beamforming and
the 4 processing methods. All images are displayed on a 60dB dynamic range.

Fig. 5-15. In-vivo images of a subxiphoid view at end-diastole for standard DAS beamforming and
the 4 processing methods. All images are displayed on a 60dB dynamic range.
98

Fig. 5-16. Final normalized cross-correlation coefficient matrices of a subxiphoid view at end-
systole for the 4 processing methods.

Fig. 5-17. Final normalized cross-correlation coefficient matrices of a subxiphoid view at end-
diastole for the 4 processing methods.
MAX Coefficient
MPAX Coefficient PAX Coefficient
DAX Coefficient
MAX Coefficient
MPAX Coefficient PAX Coefficient
DAX Coefficient
99

TABLE 5-3. Summary of CNR Values for Echocardiography

The 3 performance metrics, contrast, CNR, and speckle SNR, shown in Fig. 5-18 were
calculated as a function of the L value from the 18 frames of MAX images of an apical four-
chamber view. The results show that as the L value is increased, contrast decreases while speckle
SNR increases. CNR gradually increases until it reaches its maximum at L = 5 and starts to
decrease for L > 5. Based on these 3 measures, L = 3 was found to be the optimal value. Similar
analysis on MPAX images, which is not presented in this paper, also demonstrated that L = 3
resulted in the best performance. Hence, L = 3 was chosen for all MAX and MPAX images
presented in this paper. Examples of MAX images formed with different values of L in
comparison to standard DAS beamforming are shown Fig. 5-19. Note that L = 1 shows highest
contrast, but it is overly aggressive as it suppresses much of the speckle signals, leading to a low
speckle SNR. On the other hand, L = 10 seems to preserve the speckle signals much better at the
cost of decreased contrast and CNR.

100

Fig. 5-18. Mean a) contrast, b) contrast-to-noise ratio (CNR) and c) speckle signal-to-noise ratio
(speckle SNR) calculated in 18 frames of MAX images as a function of the L value. Standard DAS
beamforming (shown in blue) are used as a reference.

Fig. 5-19. In-vivo standard DAS and MAX images of an apical four-chamber view at end-systole
with L=1, 3, and 10. All images are shown on a 60 dB dynamic range.

a) b)
c)
DAS
MAX
(L=1) MAX
(L=3) MAX
(L=10)
101

5.3.4 In-vivo Evaluation in Abdominal Imaging
Fig. 5-20 shows long axis view images of an abdominal aorta from one volunteer for
standard DAS beamforming and the 4 processing methods. All images are displayed on a 60 dB
dynamic range. Fig. 5-21 shows the cross-correlation coefficient matrices corresponding to the 4
processing methods. CNR values were calculated for all processing methods and summarized in
Table 5-4. Standard DAS beamforming showed limited contrast due to abdominal clutter with a
CNR of 2.6. Percent CNR improvements with DAX and PAX were only 19% and 7%,
respectively with a large amount of clutter remaining in the images. The cross-correlation
coefficient matrices for DAX and PAX shown in Fig. 5-21 also illustrate that phase differences
in the two beamformed RF signals were affected by the high levels of abdominal clutter.
However, MAX and MPAX each achieved CNR improvements of 77% and 73% and
significantly enhanced the visibility of the target. Their cross-correlation coefficient matrices
also confirm improved clutter suppression.

TABLE 5-4. Summary of CNR Values Abdominal Imaging

102

Fig. 5-20. In-vivo long-axis view images of the abdominal aorta for standard DAS beamforming and
the 4 processing methods. All images are displayed on a 60dB dynamic range.

Fig. 5-21. Final normalized cross-correlation coefficient matrices of a long axis view of the
abdominal aorta for the 4 processing methods.
MAX Coefficient
MPAX Coefficient PAX Coefficient
DAX Coefficient
103

5.4 Conclusions and Future Work
The results from simulation, experiment, and in-vivo imaging presented in this work
show that multi apodization techniques, such as MAX and MPAX, are highly effective and
robust in suppression of clutter due to reverberation effects. The experimental results suggest that
while DAX, PAX, MAX, and MPAX are all highly robust with no or little reverberation clutter,
MAX and MPAX are much more robust than DAX and PAX in the presence of strong
reverberation clutter. Using a custom sponge phantom and a copper wire mesh to mimic in-vivo
reverberation clutter, the experimental results from this study showed that MAX and MPAX
yielded CNR improvements of 252% and 281%, respectively while DAX and PAX each
achieved 100% and 137%.
Initial in-vivo results from echocardiography and abdominal imaging presented in this
study confirmed the experimental results from the custom sponge phantom. MAX and MPAX
consistently showed superior performance over DAX and PAX in apical four-chamber view and
subxiphoid view images of the heart at end-systole and at end-diastole. Similarly, long axis view
images of the abdominal aorta also showed 77 % and 73% CNR improvements for MAX and
MPAX, which are far greater than those for DAX and PAX.
Future work involves completing the clinical evaluation of these techniques on more
patients. Data sets from only one volunteer were available for this study, but at least 10 patients
will be recruited in the future to test whether or not the improvements in image contrast from the
multi apodization techniques are statistically significant. Also, a cardiologist’s subjective
evaluation will be obtained to determine whether or not the proposed techniques improve border
104

definition of heart chambers, visualization of the pulmonary artery and aortic valves, and cardiac
function. Furthermore, additional abdominal targets, such as the gall bladder and hepatic blood
vessels, will be imaged and a radiologist’s subjective assessment of the overall image quality
will be obtained for performance evaluation to demonstrate the feasibility of these techniques.

105

Chapter 6 Conclusions and Future Work

6.1 Conclusions
The major objective of this dissertation was to develop a robust clutter suppression
technique for contrast enhancement in ultrasound imaging based on a previously proposed
technique known as Dual Apodization with Cross-correlation (DAX). The novelty of the DAX
algorithm is that it aims to improve ultrasound image contrast by means of two distinct receive
(RX) apodizations to generate two different point spread functions having similar mainlobe
signals but very different clutter patterns. Particularly, using the N-N alternationg apodization
schme, DAX introduces grating lobes, which are often regarded as undesirable, and takes
advantage of the phase differences in these grating lobes to suppress clutter.
Although DAX provides a simple, elegant approach to clutter suppression, its
performance in terms of contrast-to-noise ratio (CNR) improvement was shown to decrease with
increasing aberration strength and high levels of near-field reverberation clutter, often resulting
in image artifacts in the form of black spots. To overcome its inherent limitations, I have
proposed in this dissertation, combining DAX with two different imaging techniques, a phase
aberration correction (PAC) method based on nearest-neighbor cross-correlation (NNCC), and
106

harmonic imaging (HI). Such an integrated approach was shown to be highly robust in varying
levels of phase aberration and achieve dramatic improvements in image contrast.
Furthermore, I have proposed a few different modifications and extensions of DAX for
further improvements in the algorithm itself. Phase Apodization with Cross-correlation (PAX) is
a new technique which is, to the best of my knowledge, the first attempt to adopt the concept of
sinusoidal phase grating in optics (Goodman, 1996) in medical ultrasound. This technique is
similar to DAX in utilizing two complementary RX apodizations, but different from DAX in that
it uses sinusoidal time or phase delays in the channel RF data instead of amplitude weightings.
By selecting proper values for the relevant parameters, PAX allows for much more precise and
flexible control of the grating lobe magnitudes and locations. Extensions of DAX and PAX each
known as Multi Apodization with Cross-correlation (MAX) and Multi Phase Apodization with
Cross-correlation (MPAX) were also presented in this dissertation for increased robustness in the
presence of near-field reverberation clutter. Taking advantage of the phase diversity from
multiple apodization pairs, both MAX and MPAX were shown to generate a more reliable
weighting matrix that results in larger CNR improvements compared to DAX and PAX.
Performance of these methods were evaluated and compared in simulation, experiment with a
custom sponge phantom as well as in-vivo for echocardiography and abdominal imaging.

107

6.2 Future Work
6.2.1 Real-time GPU-based beamforming with MAX and MPAX
Recent advances in computing power realized by the development of graphics processing
units (GPU) have made large-scale scientific computations much more feasible for real-time or
pseudo-real-time purposes. This is mainly due to the parallel architecture of the GPUs where
tasks can be partitioned and executed in parallel. Since ultrasound beamforming and signal
processing involve a significant amount of computations on raw RF data that can be performed
in parallel instead of in series on a single CPU, they can clearly benefit from GPUs. Several
groups have already reported using GPUs in different applications in ultrasound imaging. For
example, Rosenzweig et al (Rosenzweig et al, 2011) have shown that real-time estimation and
display of tissue displacements involved in acoustic radiation force impulse (ARFI) imaging, an
imaging technique for investigating the mechanical properties of soft tissues, are feasible when
GPUs are used. Chang et al (Chang et al, 2009) has demonstrated that color Doppler signal
processing algorithms can be implemented on a GPU and generate images comprising 500 scan
lines × 128 range samples at a frame rate of 160 fps. More recently, Minimum variance
beamforming (MVBF), which has potentials to generate high quality ultrasound images at the
expense of tremendous computing power due to the calculation of aperture weighting functions
which depend on statistics of received echo signals, has been realized in real-time using a GPU
(Chen et al, 2011).
108

Since both MAX and MPAX involve repeated computations of zero-lag normalized
cross-correlation coefficients between two beamformed RF signals in order to generate a
weighting matrix on a pixel-by-pixel basis, they are well-suited for parallel computing with
GPUs. Currently, the offline computation times for MAX and MPAX on one frame of image in
MATLAB, are 10 to 15 minutes depending on the number of image lines, the sampling
frequency, the imaging depth, and the 2D kernel size for cross-correlation. However, it is
anticipated that the computation time may be significantly reduced to at least hundreds of
miliseconds with GPU implementation.
MAX and MPAX can be implemented and performed on a NVIDIA GTX 285 using
Compute unified Device Architecture (CUDA) to reach real-time or near real-time processing
and display. The overall work flow for GPU-based beamforming and MAX/MPAX processing is
summarized in Fig. 6-1. In order to fully utilize the power of the GPU, it will be necessary to
evaluate the efficiency of these methods and make modifications to or redesign these algorithms
to work most efficiently in a parallel environment. The ability to perform MAX and MPAX real-
time or near real-time will become particularly important when used in clinics as the physician
needs to adjust probe positions and orientations based on the current image displayed on the
screen to get the best view for accurate diagnosis.
Other adaptive imaging techniques, such as the NNCC-based phase aberration correction
method presented in chapter 2, demands much greater computing power than DAX since raw RF
data need to be first up-sampled to at least 180MHz to achieve a finer delay resolution for
accurate estimation of aberrator profile and cross-correlation needs to be performed for every
neighboring element pairs at the interpolated frequency for each image line. For this reason,
109

developing a system capable of performing phase aberration correction in real-time has been
recognized as a great challenge in adaptive imaging and the best performance reported in
literature today is 2 fps with 1D arrays and up to 0.81 fps for 1.75D arrays by incorporating the
ability to compensate for phase errors at multiple beam locations (Dahl et al, 2006). However,
this method is highly parallelizable as well since aberrator profile estimation by means of cross-
correlation can be computed simultaneously using multiple compute threads in a GPU.

Fig. 6-1. The work flow for real-time GPU-based software beamforming with MAX or
MPAX.

110

6.2.2 Combination with Spatial Matched Filtering
One of the current limitations of MAX and MPAX is its reduced effectiveness away from
the transmit focus. As the transmit beam diverges away from the transmit focus, while still
improving contrast compared to standard DAS beamforming, the performance of MAX and
MPAX begins to decrease leading to a non-uniform image quality and contrast. Multiple transmit
firing may be used to overcome this limitation, but at the cost of reduced frame rate. A more
elegant approach would be to adopt a different beamforming method known as Spatial Matched
Filtering (SMF) proposed by Kim et al (Kim et al, 2006), which is designed to focus both
transmit and receive beams at all imaging depths by spatially match-filtering channel RF data
prior to summation. By combining MAX or MPAX with SMF beamforming, image contrast
enhancements are expected not only in the transmit depth of focus, but all imaging depths. The
performance of the combined MAX/MPAX – SMF method will be investigated initially using
Rayleigh-Sommerfeld analysis, Field II simulations, and experimental data from a tissue
mimicking phantom, with an ultimate goal of demonstrating its feasibility in-vivo for
echocardiography and abdominal imaging.

111

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Abstract (if available)

Abstract Ultrasound is one of the most widely used imaging modalities in clinics today. Despite its numerous advantages, ultrasound often suffers from poor image contrast, making visualization of anatomical structures difficult. In order to address this problem, a novel beamforming technique called Dual Apodization with Cross‐correlation (DAX), which can achieve significant improvements in ultrasound image contrast, was proposed. The novelty in DAX is that, instead of a single receive apodization utilized in conventional delay‐and‐sum (DAS) beamforming, it uses two distinct receive apodizations to generate two point spread functions having similar mainlobe signals but very different clutter patterns. The differences in the clutter patterns can then be detected by means of normalized cross‐correlation, and the coefficients can be multiplied with the standard DAS beamformed RF data to suppress contributions of clutter without any comprise in spatial resolution. Although this technique has potentials for better image quality and hence, more accurate diagnosis, the robustness of the algorithm in the presence of high levels of phase aberration and reverberation clutter needs to be improved. The contributions of this dissertation include demonstrating the limitations of DAX, proposing several new strategies to overcome such limitations, and evaluating their performance in simulation, tissue‐mimicking phantom and in‐vivo. Since DAX requires a good focusing quality for better clutter suppression, one of these new strategies is a method that combines DAX with a phase aberration correction technique which aims to restore some of the coherence lost by sound speed inhomogeneities in soft tissues. The second method proposed in this dissertation aims to improve the performance by employing an approach that combines DAX with harmonic imaging, which has been shown to produce reduced effects of phase aberration and reverberation clutter. ❧ Furthermore, a modified version of DAX called Multi‐Apodization with Cross‐correlation (MAX) as well as a new technique called Multi‐Phase Apodization with Cross‐correlation (MPAX), which utilizes multiple phase apodization pairs, are proposed and their performance is evaluated both in phantom and in‐vivo. In summary, this dissertation describes novel beamforming techniques that can achieve a large improvement in image contrast and demonstrates their feasibility and potentials if successfully implemented in commercial scanners used in clinics.

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Asset Metadata

Creator Shin, Junseob (author)

Core Title Novel beamforming techniques for robust contrast enhancement in ultrasound imaging

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 05/19/2014

Defense Date 03/27/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag apodization,beamforming,clutter suppression,contrast,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Yen, Jesse T. (committee chair), Hashemi, Hossein (committee member), Marmarelis, Vasilis Z. (committee member), Zhou, Qifa (committee member)

Creator Email jss003@gmail.com,junseobs@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-413764

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