Mathematical Introduction to Compressive Sensing

• 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.

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)