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A Mathematical Introduction to Compressive Sensing

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 domai...

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Bibliographic Details
Main Authors: Foucart, Simon, Rauhut, Holger (Author)
Format: eBook
Language:English
Published: New York, NY Birkhäuser 2013, 2013
Edition:1st ed. 2013
Series:Applied and Numerical Harmonic Analysis
Subjects:
Functional Analysis
Computer Science / Mathematics
Mathematics / Data Processing
Mathematical Applications In Computer Science
Computational Science And Engineering
Signal, Speech And Image Processing
Telecommunication
Communications Engineering, Networks
Signal Processing
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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

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