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020 _a9780817649487
_9978-0-8176-4948-7
024 7 _a10.1007/978-0-8176-4948-7
_2doi
050 4 _aQA71-90
072 7 _aPDE
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aMAT003000
_2bisacsh
082 0 4 _a004
_223
100 1 _aFoucart, Simon.
_eauthor.
245 1 2 _aA Mathematical Introduction to Compressive Sensing
_h[electronic resource] /
_cby Simon Foucart, Holger Rauhut.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Birkhäuser,
_c2013.
300 _aXVIII, 625 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied and Numerical Harmonic Analysis,
_x2296-5009
505 0 _a1 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.
520 _aAt 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.
650 0 _aMathematics.
650 0 _aComputer science
_xMathematics.
650 0 _aFunctional analysis.
650 0 _aComputer mathematics.
650 0 _aElectrical engineering.
650 1 4 _aMathematics.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aSignal, Image and Speech Processing.
650 2 4 _aMath Applications in Computer Science.
650 2 4 _aCommunications Engineering, Networks.
650 2 4 _aFunctional Analysis.
700 1 _aRauhut, Holger.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817649470
830 0 _aApplied and Numerical Harmonic Analysis,
_x2296-5009
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4948-7
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c43148
_d43148