A Mathematical Introduction to Compressive Sensing

  • Simon Foucart
  • Holger Rauhut

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Simon Foucart, Holger Rauhut
    Pages 1-39
  3. Simon Foucart, Holger Rauhut
    Pages 41-59
  4. Simon Foucart, Holger Rauhut
    Pages 61-75
  5. Simon Foucart, Holger Rauhut
    Pages 77-110
  6. Simon Foucart, Holger Rauhut
    Pages 111-131
  7. Simon Foucart, Holger Rauhut
    Pages 133-174
  8. Simon Foucart, Holger Rauhut
    Pages 175-199
  9. Simon Foucart, Holger Rauhut
    Pages 201-269
  10. Simon Foucart, Holger Rauhut
    Pages 271-310
  11. Simon Foucart, Holger Rauhut
    Pages 311-330
  12. Simon Foucart, Holger Rauhut
    Pages 331-365
  13. Simon Foucart, Holger Rauhut
    Pages 367-433
  14. Simon Foucart, Holger Rauhut
    Pages 435-458
  15. Simon Foucart, Holger Rauhut
    Pages 459-473
  16. Simon Foucart, Holger Rauhut
    Pages 475-513
  17. Back Matter
    Pages 515-625

About this book

Introduction

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. Key features include:

·         The first textbook completely devoted to the topic of compressive sensing

·         Comprehensive treatment of the subject, including background material from probability theory, detailed proofs of the main theorems, and an outline of possible applications

·         Numerous exercises designed to help students understand the material

·         An extensive bibliography with over 500 references that guide researchers through the literature

With only moderate prerequisites, A Mathematical Introduction to Compressive Sensing 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.

Keywords

compressed sampling compressed sensing compressive sampling greedy algorithms optimization theory probability theory random matrices sampling theory signal processing sparse recovery

Authors and affiliations

  • Simon Foucart
    • 1
  • Holger Rauhut
    • 2
  1. 1.Dept. MathematicsDrexel University 269 Korman CenterPhiladelphiaUSA
  2. 2.Lehrstuhl für Mathematik C (Analysis)RWTH Aachen UniversityAachenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4948-7
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4947-0
  • Online ISBN 978-0-8176-4948-7
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • About this book