ENGLISH

A Mathematical Introduction to Compressive Sensing

By Simon Foucart , Holger Rauhut

Book information

Publisher
Birkhäuser
Year
2013
ISBN
0817649476, 978-0-8176-4947-0, 978-0-8176-4948-7
Language
english
Format
PDF
Filesize
4 MB (3951901 bytes)
Series
Applied and Numerical Harmonic Analysis
Pages
625\634
Library
kolxoz
Time added
2017-10-15 16:00:00

Description

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. Front Matter....Pages i-xviii An Invitation to Compressive Sensing....Pages 1-39 Sparse Solutions of Underdetermined Systems....Pages 41-59 Basic Algorithms....Pages 61-75 Basis Pursuit....Pages 77-110 Coherence....Pages 111-131 Restricted Isometry Property....Pages 133-174 Basic Tools from Probability Theory....Pages 175-199 Advanced Tools from Probability Theory....Pages 201-269 Sparse Recovery with Random Matrices....Pages 271-310 Gelfand Widths of ℓ 1 -Balls....Pages 311-330 Instance Optimality and Quotient Property....Pages 331-365 Random Sampling in Bounded Orthonormal Systems....Pages 367-433 Lossless Expanders in Compressive Sensing....Pages 435-458 Recovery of Random Signals using Deterministic Matrices....Pages 459-473 Algorithms for ℓ 1 -Minimization....Pages 475-513 Back Matter....Pages 515-625

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