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Table of Contents
Intro; Preface; Contents; 1 Sparse Representations; 1.1 The Sparse Model; 1.2 Algorithms; 1.3 Orthogonal Matching Pursuit; 1.4 Algorithms for Basis Pursuit: FISTA; 1.5 Guarantees; 1.6 The Choice of a Dictionary: Fixed vs Learned; Problems; 2 Dictionary Learning Problem; 2.1 The Optimization Problem; 2.2 An Analysis of the DL Problem; 2.3 Test Problems; 2.3.1 Representation Error; 2.3.2 Dictionary Recovery; 2.4 Applications: A Quick Overview; 2.4.1 Denoising; 2.4.2 Inpainting; 2.4.3 Compression; 2.4.4 Compressed Sensing; 2.4.5 Classification; Problems; 3 Standard Algorithms.
3.1 Basic Strategy: Alternating Optimization3.2 Sparse Coding; 3.3 Simple Descent Methods; 3.3.1 Gradient Descent; 3.3.2 Coordinate Descent; 3.4 Method of Optimal Directions (MOD); 3.5 K-SVD; 3.6 Parallel Algorithms; 3.7 SimCO; 3.8 Refinements; 3.9 Practical Issues; 3.9.1 Initialization; 3.9.2 Dictionary Size and Other Size Parameters; 3.9.3 Unused or Redundant Atoms; 3.9.4 Randomization; 3.10 Comparisons: Theory; 3.11 Comparisons: Some Experimental Results; 3.11.1 Representation Error Results; 3.11.2 Dictionary Recovery Result; 3.11.3 Denoising Results.
3.12 Impact of Sparse Representation AlgorithmProblems; 4 Regularization and Incoherence; 4.1 Learning with a Penalty; 4.2 Regularization; 4.2.1 Sparse Coding; 4.2.2 Regularized K-SVD; 4.2.3 Comparison Between Regularized K-SVD and SimCO; 4.3 Frames; 4.4 Joint Optimization of Error and Coherence; 4.5 Optimizing an Orthogonal Dictionary; 4.6 Imposing Explicit Coherence Bounds; 4.7 Atom-by-Atom Decorrelation; Problems; 5 Other Views on the DL Problem; 5.1 Representations with Variable Sparsity Levels; 5.2 A Simple Algorithm for DL with l1 Penalty; 5.3 A Majorization Algorithm.
5.4 Proximal Methods5.5 A Gallery of Objectives; 5.6 Task-Driven DL; 5.7 Dictionary Selection; 5.8 Online DL; 5.8.1 Online Coordinate Descent; 5.8.2 RLS DL; 5.9 DL with Incomplete Data; Problems; 6 Optimizing Dictionary Size; 6.1 Introduction: DL with Imposed Error; 6.2 A General Size-Optimizing DL Structure; 6.3 Stagewise K-SVD; 6.4 An Initialization Method; 6.5 An Atom Splitting Procedure; 6.6 Clustering as a DL Tool; 6.7 Other Methods; 6.8 Size-Reducing OMP; Problems; 7 Structured Dictionaries; 7.1 Short Introduction; 7.2 Sparse Dictionaries; 7.2.1 Double Sparsity; 7.2.2 Greedy Selection.
7.2.3 Multi-Layer Sparse DL7.2.4 Multiscale Dictionaries; 7.3 Orthogonal Blocks; 7.3.1 Orthogonal Basis Training; 7.3.2 Union of Orthonormal Bases; 7.3.3 Single Block Orthogonal DL; 7.4 Shift Invariant Dictionaries; 7.4.1 Circulant Dictionaries; 7.4.2 Convolutional Sparse Coding; 7.5 Separable Dictionaries; 7.5.1 2D-OMP; 7.5.2 SeDiL; 7.6 Tensor Strategies; 7.6.1 CP Decomposition; 7.6.2 CP Dictionary Update; 7.6.3 Tensor Singular Valued Decomposition; 7.6.4 t-SVD Dictionary Update; 7.7 Composite Dictionaries; 7.7.1 Convex Approach; 7.7.2 Composite Dictionaries with Orthogonal Blocks; Problems.
3.1 Basic Strategy: Alternating Optimization3.2 Sparse Coding; 3.3 Simple Descent Methods; 3.3.1 Gradient Descent; 3.3.2 Coordinate Descent; 3.4 Method of Optimal Directions (MOD); 3.5 K-SVD; 3.6 Parallel Algorithms; 3.7 SimCO; 3.8 Refinements; 3.9 Practical Issues; 3.9.1 Initialization; 3.9.2 Dictionary Size and Other Size Parameters; 3.9.3 Unused or Redundant Atoms; 3.9.4 Randomization; 3.10 Comparisons: Theory; 3.11 Comparisons: Some Experimental Results; 3.11.1 Representation Error Results; 3.11.2 Dictionary Recovery Result; 3.11.3 Denoising Results.
3.12 Impact of Sparse Representation AlgorithmProblems; 4 Regularization and Incoherence; 4.1 Learning with a Penalty; 4.2 Regularization; 4.2.1 Sparse Coding; 4.2.2 Regularized K-SVD; 4.2.3 Comparison Between Regularized K-SVD and SimCO; 4.3 Frames; 4.4 Joint Optimization of Error and Coherence; 4.5 Optimizing an Orthogonal Dictionary; 4.6 Imposing Explicit Coherence Bounds; 4.7 Atom-by-Atom Decorrelation; Problems; 5 Other Views on the DL Problem; 5.1 Representations with Variable Sparsity Levels; 5.2 A Simple Algorithm for DL with l1 Penalty; 5.3 A Majorization Algorithm.
5.4 Proximal Methods5.5 A Gallery of Objectives; 5.6 Task-Driven DL; 5.7 Dictionary Selection; 5.8 Online DL; 5.8.1 Online Coordinate Descent; 5.8.2 RLS DL; 5.9 DL with Incomplete Data; Problems; 6 Optimizing Dictionary Size; 6.1 Introduction: DL with Imposed Error; 6.2 A General Size-Optimizing DL Structure; 6.3 Stagewise K-SVD; 6.4 An Initialization Method; 6.5 An Atom Splitting Procedure; 6.6 Clustering as a DL Tool; 6.7 Other Methods; 6.8 Size-Reducing OMP; Problems; 7 Structured Dictionaries; 7.1 Short Introduction; 7.2 Sparse Dictionaries; 7.2.1 Double Sparsity; 7.2.2 Greedy Selection.
7.2.3 Multi-Layer Sparse DL7.2.4 Multiscale Dictionaries; 7.3 Orthogonal Blocks; 7.3.1 Orthogonal Basis Training; 7.3.2 Union of Orthonormal Bases; 7.3.3 Single Block Orthogonal DL; 7.4 Shift Invariant Dictionaries; 7.4.1 Circulant Dictionaries; 7.4.2 Convolutional Sparse Coding; 7.5 Separable Dictionaries; 7.5.1 2D-OMP; 7.5.2 SeDiL; 7.6 Tensor Strategies; 7.6.1 CP Decomposition; 7.6.2 CP Dictionary Update; 7.6.3 Tensor Singular Valued Decomposition; 7.6.4 t-SVD Dictionary Update; 7.7 Composite Dictionaries; 7.7.1 Convex Approach; 7.7.2 Composite Dictionaries with Orthogonal Blocks; Problems.