TY - BOOK
AU - Foucart,Simon
AU - Rauhut,Holger
ED - SpringerLink (Online service)
TI - A Mathematical Introduction to Compressive Sensing
T2 - Applied and Numerical Harmonic Analysis,
SN - 9780817649487
AV - QA71-90
U1 - 004 23
PY - 2013///
CY - New York, NY
PB - Springer New York, Imprint: Birkhäuser
KW - Mathematics
KW - Computer science
KW - Functional analysis
KW - Computer mathematics
KW - Electrical engineering
KW - Computational Science and Engineering
KW - Signal, Image and Speech Processing
KW - Math Applications in Computer Science
KW - Communications Engineering, Networks
KW - Functional Analysis
N1 - 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
N2 - 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
UR - http://dx.doi.org/10.1007/978-0-8176-4948-7
ER -