kristen-thesis - OPTIMIZATION TECHNIQUES FOR SOLVING BASIS...

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Unformatted text preview: OPTIMIZATION TECHNIQUES FOR SOLVING BASIS PURSUIT PROBLEMS By Kristen Michelle Cheman A Thesis Submitted to the Graduate Faculty of North Carolina State University in Partial Fulfillment of the Requirements for the Degree of MASTER OF APPLIED MATHEMATICS Approved: Dr. Kartik Sivaramakrishnan, Thesis Adviser Dr. Ralph Smith, Member Dr. Ernie Stitzinger, Member North Carolina State University Raleigh, North Carolina March 29, 2006 (For Graduation May 2006) OPTIMIZATION TECHNIQUES FOR SOLVING BASIS PURSUIT PROBLEMS By Kristen Michelle Cheman An Abstract of a Thesis Submitted to the Graduate Faculty of North Carolina State University in Partial Fulfillment of the Requirements for the Degree of MASTER OF APPLIED MATHEMATICS The original of the complete thesis is on file in the Department of Mathematics Examining Committee: Dr. Kartik Sivaramakrishnan, Thesis Adviser Dr. Ralph Smith, Member Dr. Ernie Stitzinger, Member North Carolina State University Raleigh, North Carolina March 29, 2006 (For Graduation May 2006) c Copyright 2006 by Kristen Michelle Cheman All Rights Reserved ii CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Previous work on data reduction . . . . . . . . . . . . . . . . . . . . . 4 1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 Introduction to the problem . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Methods of decomposition . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Basis Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Method of Frames . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Signal Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.1 Analysis of data reduction . . . . . . . . . . . . . . . . . . . . 15 2.4.2 Analysis of signal denoising . . . . . . . . . . . . . . . . . . . 18 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 APPENDICES A. MATLAB code for minimizing the 1-norm of x . . . . . . . . . . . . . . . . 22 B. MATLAB code for minimizing the 2-norm of x . . . . . . . . . . . . . . . . 24 iii C. MATLAB codes for solving data reduction problems using MOF and BPC....
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kristen-thesis - OPTIMIZATION TECHNIQUES FOR SOLVING BASIS...

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