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CRITICALLY SAMPLED WAVELET FILTERBANKS ON GRAPHS
by
Sunil K. Narang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2012
Copyright 2012 Sunil K. Narang
Object Description
| Title | Critically sampled wavelet filterbanks on graphs |
| Author | Narang, Sunil Kumar |
| Author email | kumarsun@usc.edu;narang.sunil@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Electrical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2012-05-17 |
| Date submitted | 2012-07-24 |
| Date approved | 2012-07-24 |
| Restricted until | 2012-07-24 |
| Date published | 2012-07-24 |
| Advisor (committee chair) | Ortega, Antonio |
| Advisor (committee member) |
Krishnamachari, Bhaskar Liu, Yan |
| Abstract | Emerging data mining applications will have to operate on datasets defined on graphs. Examples of such datasets include online document networks, social networks, and transportation networks etc. The data on these graphs can be visualized as a finite collection of samples, a graph-signal which can be defined as the information attached to each node (scalar or vector values mapped to the set of vertices/edges) of the graph. Major challenges are posed by the size of these datasets, making it difficult to visualize, process, analyze and act on the information available. Wavelets have been popular for traditional signal processing problems (e.g., compression, segmentation, denoising) because they allow signal representations where a variety of trade-offs between spatial (or temporal) resolution and frequency resolution can be achieved. In this research, we seek to leverage novel basic wavelet techniques for graph data, and apply them to realistic information analytics problems. The primary contribution of this thesis is to design critically sampled wavelet filterbanks on graphs, which provide a local analysis in the graph (localized within a few hops of a target node), while capturing spectral/frequency information of the graph-signals. The graphs in our study are simple undirected graphs. We first design ""one-dimensional"" two-channel filterbanks on bipartite graphs, and then extend them to any arbitrary graph. The filterbanks come in two flavors, depending upon the chosen downsampling method: i) lifting wavelet filterbanks and ii) spectral wavelet filterbanks. For bipartite graphs we define a spectral folding phenomenon, analogous to aliasing in regular signals, that helps us define filterbank constraints in simple terms. For arbitrary graphs we propose two choices: a) to approximate the graph as a single bipartite graph and apply one-dimensional"" filterbanks, or b) to decompose the graph into multiple bipartite subgraphs and apply multi-dimensional"" filterbanks. All our proposed filterbanks designs are critically sampled and perfect reconstruction. To the best of our knowledge, no such filterbanks have been proposed before. The tools proposed in this thesis make it possible to develop i) multiresolution representations of graphs, ii) edge-aware processing of regular signals, iii) anomaly detection in datasets, and iv) sampling of large networks. |
| Keyword | digital signal processing; network theory (graphs); sampling in graphs; wavelet transforms |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Narang, Sunil Kumar |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume4/etd-NarangSuni-977.pdf |
Description
| Title | Page 1 |
| Full text | CRITICALLY SAMPLED WAVELET FILTERBANKS ON GRAPHS by Sunil K. Narang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2012 Copyright 2012 Sunil K. Narang |
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