A Mathematical Introduction to Compressive Sensing

Front Cover
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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

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

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

Other editions - View all

Common terms and phrases