Mathematical Introduction to Compressive Sensing

AvSimon Foucart,Holger Rauhut

Inbunden, Engelska, 2013

Del i serien Applied and Numerical Harmonic Analysis

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2013-08-08
Mått:160 x 242 x 38 mm
Vikt:1 090 g
Format:Inbunden
Språk:Engelska
Serie:Applied and Numerical Harmonic Analysis
Antal sidor:625
Upplaga:2013
Förlag:Birkhauser Boston Inc
ISBN:9780817649470

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Recensioner i media

From the book reviews: "As a textbook it offers great flexibility for the instructor and can be used for both introductory and advanced courses in compressed sensing. ... The book can be highly recommended for teaching purposes, and the homework problems are really excellent. As an encyclopedia the book is very comprehensive and offers detailed proofs and discussions. ... It is expected that this book will become a classical reference source in the field." (Anders C. Hansen, Mathematical Reviews, November, 2014)

Innehållsförteckning

1 An Invitation to Compressive Sensing.- 2 Sparse Solutions of Underdetermined Systems.- 3 Basic Algorithms.- 4 Basis Pursuit.- 5 Coherence.- 6 Restricted Isometry Property.- 7 Basic Tools from Probability Theory.- 8 Advanced Tools from Probability Theory.- 9 Sparse Recovery with Random Matrices.- 10 Gelfand Widths of l1-Balls.- 11 Instance Optimality and Quotient Property.- 12 Random Sampling in Bounded Orthonormal Systems.- 13 Lossless Expanders in Compressive Sensing.- 14 Recovery of Random Signals using Deterministic Matrices.- 15 Algorithms for l1-Minimization.- Appendix A Matrix Analysis.- Appendix B Convex Analysis.- Appendix C Miscellanea.- List of Symbols.- References.