# A Mathematical Introduction to Compressive Sensing

Springer Science & Business Media, Aug 13, 2013 - Computers - 625 pages

At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians.

A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.

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### Contents

 Chapter 1 1 An Invitation to Compressive Sensing Chapter 41 2 Sparse Solutions of Underdetermined Systems Chapter 60 3 Basic Algorithms Chapter 77 4 Basis Pursuit Chapter 111 5 Coherence Chapter 132 6 Restricted Isometry Property Chapter 175 7 Basic Tools from Probability Theory Chapter 201 8 Advanced Tools from Probability Theory
 Chapter 434 13 Lossless Expanders in Compressive Sensing Chapter 459 14 Recovery of Random Signals using Deterministic Matrices Chapter 15 Algorithms for ℓ1Minimization 475 Appendix 514 A Matrix Analysis Appendix 543 B Convex Analysis Appendix 573 C Miscellanea List of Symbols 589 References 593

 Chapter 270 9 Sparse Recovery with Random Matrices Chapter 10 Gelfand Widths of ℓ1Balls 311 Chapter 331 11 Instance Optimality and Quotient Property Chapter 367 12 Random Sampling in Bounded Orthonormal Systems
 Applied and Numerical Harmonic Analysis 63 Volumes 617 Index 621 Copyright