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131104t20132013xxe ||| |||| 00| 0 eng d |
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PPN172681324 |
| 020 |
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|a 9780817649470 (rel.)
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| 020 |
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|a 9781493900633 (br.)
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| 024 |
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|a 9781493900633
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| 024 |
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|a 9780817649470
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| 041 |
0 |
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|a eng
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| 082 |
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|a 004
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| 084 |
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|a G.1
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| 084 |
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|a 94-01. 2010
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| 084 |
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|a 94A08. 2010
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| 084 |
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|a 94A12. 2010
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| 100 |
1 |
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|a Foucart, Simon.
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| 245 |
1 |
0 |
|a A mathematical introduction to compressive sensing
|c Simon Foucart, Holger Rauhut.
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| 260 |
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|a New York :
|b Birkhäuser :
|b Springer.
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| 260 |
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|c C 2013.
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| 300 |
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|a 1 vol. (XVIII-625 p.) :
|b fig., ill., phot., couv. ill. en coul. ;
|c 24 cm.
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| 490 |
1 |
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|a Applied and numerical harmonic analysis
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| 504 |
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|a Bibliogr. p. 593-615. Index
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| 505 |
0 |
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|a 1 An Invitation to Compressive Sensing -- 1.1 What is Compressive Sensing? -- 1.2 Applications, Motivations, and Extensions -- 1.3 Overview of the Book -- 2 Sparse Solutions of Underdetermined Systems -- 2.1 Sparsity and Compressibility -- 2.2 Minimal Number of Measurements -- 2.3 NP-Hardness of 0-Minimization -- 3 Basic Algorithms -- 3.1 Optimization Methods -- 3.2 Greedy Methods . -- 3.3 Thresholding-Based Methods -- 4 Basis Pursuit -- 4.1 Null Space Property -- 4.2 Stability -- 4.3 Robustness -- 4.4 Recovery of Individual Vectors -- 4.5 The Projected Cross-Polytope -- 4.6 Low-Rank Matrix Recovery -- 5 Coherence -- 5.1 Definitions and Basic Properties -- 5.2 Matrices with Small Coherence -- 5.3 Analysis of Orthogonal Matching Pursuit -- 5.4 Analysis of Basis Pursuit -- 5.5 Analysis of Thresholding Algorithms -- 6 Restricted Isometry Property -- 6.1 Definitions and Basic Properties -- 6.2 Analysis of Basis Pursuit -- 6.3 Analysis of Thresholding Algorithms -- 6.4 Analysis of Greedy Algorithms -- 7 Basic Tools from Probability Theory -- 7.1 Essentials from Probability -- 7.2 Moments and Tails -- 7.3 Cramer s Theorem and Hoeffding s Inequality -- 7.4 Subgaussian Random Variables -- 7.5 Bernstein Inequalities -- 8 Advanced Tools from Probability Theory -- 8.1 Expectation of Norms of Gaussian Vectors -- 8.2 Rademacher Sums and Symmetrization -- 8.3 Khintchine Inequalities -- 8.4 Decoupling -- 8.5 Noncommutative Bernstein Inequality -- 8.6 Dudley s Inequality -- 8.7 Slepian s and Gordon s Lemmas -- 8.8 Concentration of Measure -- 8.9 Bernstein Inequality for Suprema of Empirical Processes -- 9 Sparse Recovery with Random Matrices -- 9.1 Restricted Isometry Property for Subgaussian Matrices -- 9.2 Nonuniform Recovery -- 9.3 Restricted Isometry Property for Gaussian Matrices -- 9.4 Null Space Property for Gaussian Matrices -- 9.5 Relation to Johnson Lindenstrauss Embeddings -- 10 Gelfand Widths of 1-Balls -- 10.1 Definitions and Relation to Compressive Sensing -- 10.2 Estimate for the Gelfand Widths of 1-Balls -- 10.3 Applications to the Geometry of Banach Spaces -- 11 Instance Optimality and Quotient Property -- 11.1 Uniform Instance Optimality -- 11.2 Robustness and Quotient Property -- 11.3 Quotient Property for Random Matrices -- 11.4 Nonuniform Instance Optimality -- 12 Random Sampling in Bounded Orthonormal Systems -- 12.1 Bounded Orthonormal Systems -- 12.2 Uncertainty Principles and Lower Bounds -- 12.3 Nonuniform Recovery: Random Sign Patterns -- 12.4 Nonuniform Recovery: Deterministic Sign Patterns -- 12.5 Restricted Isometry Property -- 12.6 Discrete Bounded Orthonormal Systems -- 12.7 Relation to the 1-Problem -- 13 Lossless Expanders in Compressive Sensing -- 13.1 Definitions and Basic Properties -- 13.2 Existence of Lossless Expanders -- 13.3 Analysis of Basis Pursuit -- 13.4 Analysis of an Iterative Thresholding Algorithm -- 13.5 Analysis of a Simple Sublinear-Time Algorithm -- 14 Recovery of Random Signals using Deterministic Matrices -- 14.1 Conditioning of Random Submatrices -- 14.2 Sparse Recovery via 1-Minimization -- 15 Algorithms for 1-Minimization -- 5.1 The Homotopy Method -- 15.2 Chambolle and Pock s Primal-Dual Algorithm -- 15.3 Iteratively Reweighted Least Squares -- A Matrix Analysis -- A.1 Vector and Matrix Norms -- A.2 The Singular Value Decomposition -- A.3 Least Squares Problems -- A.4 Vandermonde Matrices -- A.5 Matrix Function -- B Convex Analysis -- B.1 Convex Sets -- B.2 Convex Functions -- B.3 The Convex Conjugate -- B.4 The Subdifferential -- B.5 Convex Optimization Problems -- B.6 Matrix Convexity -- C Miscellanea -- C.1 Fourier Analysis -- C.2 Covering Numbers -- C.3 The Gamma Function and Stirling s Formula -- C.4 The Multinomial Theorem
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| 650 |
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|a Analyse informatique
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| 650 |
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|a Informatique
|x Mathématiques
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| 650 |
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|a Données
|x Compression (télécommunications)
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| 650 |
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|a Traitement du signal
|x Techniques numériques
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| 650 |
|
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|a Algorithmes optimaux
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| 650 |
|
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|a Échantillonnage (statistique)
|
| 700 |
1 |
|
|a Rauhut, Holger.
|4 aut
|
| 776 |
0 |
|
|0 172416795
|t A mathematical introduction to compressive sensing
|f by Simon Foucart, Holger Rauhut.
|e 1st ed. 2013.
|c New York, NY
|n Springer New York
|d 2013
|s Applied and Numerical Harmonic Analysis
|z 978-0-8176-4948-7
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| 997 |
|
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|0 580782
|1 Livre papier
|a Ressource papier
|c 0/Orléans/
|c 1/Orléans/IDP/
|z Orléans, IDP, 8091 FOU
|
