Author

Joshua Booth

Defense Date

8-17-2010

Graduation Date

2010

Availability

Immediate Access

Submission Type

thesis

Degree Name

MS

Department

Computational Mathematics

School

McAnulty College and Graduate School of Liberal Arts

Committee Chair

Carl Toews

Committee Member

Donald Simon

Committee Member

Karl Wimmer

Committee Member

Jeffrey Jackson

Keywords

compressive sensing, expander graphs, random matrix, signal processing, sparse signal

Abstract

This work is an expository overview of certain key elements in the area of compressive sensing. As a sub-discipline of signal processing, compressive sensing is concerned with both sampling and reconstruction techniques. In this expository, sampling will center on random matrices and expander graphs, while reconstruction will use multiple numerical optimization techniques. Although theoretical performance bounds for these techniques can be found scattered throughout the published literature, there are few practical rules for concrete problems. This thesis helps fill this gap by experimenting on the asymptotic bounds of the number of measurements needed to guarantee perfect reconstruction. These numerical experiments help to identify specific sensing regimes in which performance begin to break down.

Format

PDF

Language

English

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