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A Mathematical Introduction to Compressive Sensing |  |
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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 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.
媒体推荐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) 目录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
网友对A Mathematical Introduction to Compressive Sensing的评论
非常好的一本书，就是贵了点，不过物有所值
This book may be a little hard at the begining if your mathematical background is not so strong, but the appendices should be enough to get involved easily into the book.
It is very well explained in the key concepts and a little trivial in the concepts the authors think are not so important.
I highly recommend this book if you are a beginner and want to get involved in the CS researching world.
If you would like to know the mathematical theory of compressive sensing, this is a really nice book to read. It contains most of the recent techniques (random matrices, convex optimization) to establish the theoretic compressive sensing as well as numerical algorithms. Some of the methods are also useful in low-rank matrices recovery and matrix completion. Strongly recommend this book for researcher in this field.
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