04172nam a22005417a 4500001001500000003000900015005001700024007001500041008004100056020003700097024003500134050001200169072001600181072002300197072002300220082001200243100002900255245011400284264007100398300003600469336002600505337002600531338003600557347002400593490005600617505071000673520161001383650001702993650003503010650002503045650002603070650002803096650001703124650004303141650004103184650004303225650004203268650002503310700002903335710003403364773002003398776003603418830005603454856004803510912001403558942004103572999001703613sulb-eb0021056BD-SySUS20160413122128.0cr nn 008mamaa130808s2013 xxu| s |||| 0|eng d a97808176494879978-0-8176-4948-77 a10.1007/978-0-8176-4948-72doi 4aQA71-90 7aPDE2bicssc 7aCOM0140002bisacsh 7aMAT0030002bisacsh04a0042231 aFoucart, Simon.eauthor.12aA Mathematical Introduction to Compressive Sensingh[electronic resource] /cby Simon Foucart, Holger Rauhut. 1aNew York, NY :bSpringer New York :bImprint: Birkhäuser,c2013. aXVIII, 625 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aApplied and Numerical Harmonic Analysis,x2296-50090 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. 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. 0aMathematics. 0aComputer sciencexMathematics. 0aFunctional analysis. 0aComputer mathematics. 0aElectrical engineering.14aMathematics.24aComputational Science and Engineering.24aSignal, Image and Speech Processing.24aMath Applications in Computer Science.24aCommunications Engineering, Networks.24aFunctional Analysis.1 aRauhut, Holger.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817649470 0aApplied and Numerical Harmonic Analysis,x2296-500940uhttp://dx.doi.org/10.1007/978-0-8176-4948-7 aZDB-2-SMA 2Dewey Decimal ClassificationceBooks c43148d43148