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A mathematical introduction to compressive sensing
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| Auteurs principaux : | , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | A mathematical introduction to compressive sensing / Simon Foucart, Holger Rauhut |
| Publié : |
New York :
Birkhäuser
, copyright 2013 Springer |
| Description matérielle : | 1 vol. (XVIII-625 p.) |
| Collection : | Applied and numerical harmonic analysis (Print) |
| Sujets : | |
| Documents associés : | Autre format:
A mathematical introduction to compressive sensing |
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| 200 | 1 | |a A mathematical introduction to compressive sensing |f Simon Foucart, Holger Rauhut | |
| 210 | |a New York |c Birkhäuser |c Springer |d copyright 2013 | ||
| 215 | |a 1 vol. (XVIII-625 p.) |c ill. |d 24 cm | ||
| 225 | 0 | |a Applied and numerical harmonic analysis | |
| 320 | |a Bibliogr. p. 593-615. Index | ||
| 359 | 2 | |b 1 An Invitation to Compressive Sensing |c 1.1 What is Compressive Sensing? |c 1.2 Applications, Motivations, and Extensions |c 1.3 Overview of the Book |b 2 Sparse Solutions of Underdetermined Systems |c 2.1 Sparsity and Compressibility |c 2.2 Minimal Number of Measurements |c 2.3 NP-Hardness of 0-Minimization |b 3 Basic Algorithms |c 3.1 Optimization Methods |c 3.2 Greedy Methods . |c 3.3 Thresholding-Based Methods |b 4 Basis Pursuit |c 4.1 Null Space Property |c 4.2 Stability |c 4.3 Robustness |c 4.4 Recovery of Individual Vectors |c 4.5 The Projected Cross-Polytope |c 4.6 Low-Rank Matrix Recovery |b 5 Coherence |c 5.1 Definitions and Basic Properties |c 5.2 Matrices with Small Coherence |c 5.3 Analysis of Orthogonal Matching Pursuit |c 5.4 Analysis of Basis Pursuit |c 5.5 Analysis of Thresholding Algorithms |b 6 Restricted Isometry Property |c 6.1 Definitions and Basic Properties |c 6.2 Analysis of Basis Pursuit |c 6.3 Analysis of Thresholding Algorithms |c 6.4 Analysis of Greedy Algorithms |b 7 Basic Tools from Probability Theory |c 7.1 Essentials from Probability |c 7.2 Moments and Tails |c 7.3 Cramer s Theorem and Hoeffding s Inequality |c 7.4 Subgaussian Random Variables |c 7.5 Bernstein Inequalities |b 8 Advanced Tools from Probability Theory |c 8.1 Expectation of Norms of Gaussian Vectors |c 8.2 Rademacher Sums and Symmetrization |c 8.3 Khintchine Inequalities |c 8.4 Decoupling |c 8.5 Noncommutative Bernstein Inequality |c 8.6 Dudley s Inequality |c 8.7 Slepian s and Gordon s Lemmas |c 8.8 Concentration of Measure |c 8.9 Bernstein Inequality for Suprema of Empirical Processes |b 9 Sparse Recovery with Random Matrices |c 9.1 Restricted Isometry Property for Subgaussian Matrices |c 9.2 Nonuniform Recovery |c 9.3 Restricted Isometry Property for Gaussian Matrices |c 9.4 Null Space Property for Gaussian Matrices |c 9.5 Relation to Johnson Lindenstrauss Embeddings |b 10 Gelfand Widths of 1-Balls |c 10.1 Definitions and Relation to Compressive Sensing |c 10.2 Estimate for the Gelfand Widths of 1-Balls |c 10.3 Applications to the Geometry of Banach Spaces |b 11 Instance Optimality and Quotient Property |c 11.1 Uniform Instance Optimality |c 11.2 Robustness and Quotient Property |c 11.3 Quotient Property for Random Matrices |c 11.4 Nonuniform Instance Optimality |b 12 Random Sampling in Bounded Orthonormal Systems |c 12.1 Bounded Orthonormal Systems |c 12.2 Uncertainty Principles and Lower Bounds |c 12.3 Nonuniform Recovery: Random Sign Patterns |c 12.4 Nonuniform Recovery: Deterministic Sign Patterns |c 12.5 Restricted Isometry Property |c 12.6 Discrete Bounded Orthonormal Systems |c 12.7 Relation to the 1-Problem |b 13 Lossless Expanders in Compressive Sensing |c 13.1 Definitions and Basic Properties |c 13.2 Existence of Lossless Expanders |c 13.3 Analysis of Basis Pursuit |c 13.4 Analysis of an Iterative Thresholding Algorithm |c 13.5 Analysis of a Simple Sublinear-Time Algorithm |b 14 Recovery of Random Signals using Deterministic Matrices |c 14.1 Conditioning of Random Submatrices |c 14.2 Sparse Recovery via 1-Minimization |b 15 Algorithms for 1-Minimization |c 5.1 The Homotopy Method |c 15.2 Chambolle and Pock s Primal-Dual Algorithm |c 15.3 Iteratively Reweighted Least Squares |b A Matrix Analysis |c A.1 Vector and Matrix Norms |c A.2 The Singular Value Decomposition |c A.3 Least Squares Problems |c A.4 Vandermonde Matrices |c A.5 Matrix Function |b B Convex Analysis |c B.1 Convex Sets |c B.2 Convex Functions |c B.3 The Convex Conjugate |c B.4 The Subdifferential |c B.5 Convex Optimization Problems |c B.6 Matrix Convexity |b C Miscellanea |c C.1 Fourier Analysis |c C.2 Covering Numbers |c C.3 The Gamma Function and Stirling s Formula |c C.4 The Multinomial Theorem | |
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