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Part of: Synthesis digital library of engineering and computer science.

Series from website.

Includes bibliographical references (pages 91-104).

1. Introduction -- 1.1 Modeling natural images -- 1.2 Natural image statistics -- 1.3 Sparseness in biological vision -- 1.4 The generative model for sparse coding -- 1.5 Sparse models for image reconstruction -- 1.5.1 Dictionary design -- 1.5.2 Example applications -- 1.6 Sparse models for recognition -- 1.6.1 Discriminative dictionaries -- 1.6.2 Bag of words and its generalizations -- 1.6.3 Dictionary design with graph embedding constraints -- 1.6.4 Kernel sparse methods --

2. Sparse representations -- 2.1 The sparsity regularization -- 2.1.1 Other sparsity regularizations -- 2.1.2 Non-negative sparse representations -- 2.2 Geometrical interpretation -- 2.3 Uniqueness of l0 and its equivalence to the l1 solution -- 2.3.1 Phase transitions -- 2.4 Numerical methods for sparse coding -- 2.4.1 Optimality conditions -- 2.4.2 Basis pursuit -- 2.4.3 Greedy pursuit methods -- 2.4.4 Feature-sign search -- 2.4.5 Iterated shrinkage methods --

3. Dictionary learning: theory and algorithms -- 3.1 Dictionary learning and clustering -- 3.1.1 Clustering procedures -- 3.1.2 Probabilistic formulation -- 3.2 Learning algorithms -- 3.2.1 Method of optimal directions -- 3.2.2 K-SVD -- 3.2.3 Multilevel dictionaries -- 3.2.4 Online dictionary learning -- 3.2.5 Learning structured sparse models -- 3.2.6 Sparse coding using examples -- 3.3 Stability and generalizability of learned dictionaries -- 3.3.1 Empirical risk minimization -- 3.3.2 An example case: multilevel dictionary learning --

4. Compressed sensing -- 4.1 Measurement matrix design -- 4.1.1 The restricted isometry property -- 4.1.2 Geometric interpretation -- 4.1.3 Optimized measurements -- 4.2 Compressive sensing of natural images -- 4.3 Video compressive sensing -- 4.3.1 Frame-by-frame compressive recovery -- 4.3.2 Model-based video compressive sensing -- 4.3.3 Direct feature extraction from compressed videos --

5. Sparse models in recognition -- 5.1 A simple classification setup -- 5.2 Discriminative dictionary learning -- 5.3 Sparse-coding-based subspace identification -- 5.4 Using unlabeled data in supervised learning -- 5.5 Generalizing spatial pyramids -- 5.5.1 Supervised dictionary optimization -- 5.6 Locality in sparse models -- 5.6.1 Local sparse coding -- 5.6.2 Dictionary design -- 5.7 Incorporating graph embedding constraints -- 5.7.1 Laplacian sparse coding -- 5.7.2 Local discriminant sparse coding -- 5.8 Kernel methods in sparse coding -- 5.8.1 Kernel sparse representations -- 5.8.2 Kernel dictionaries in representation and discrimination -- 5.8.3 Combining diverse features -- 5.8.4 Application: tumor identification --

Bibliography -- Authors' biographies.

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Image understanding has been playing an increasingly crucial role in several inverse problems and computer vision. Sparse models form an important component in image understanding, since they emulate the activity of neural receptors in the primary visual cortex of the human brain. Sparse methods have been utilized in several learning problems because of their ability to provide parsimonious, interpretable, and efficient models. Exploiting the sparsity of natural signals has led to advances in several application areas including image compression, denoising, inpainting, compressed sensing, blind source separation, super-resolution, and classification.

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Title from PDF title page (viewed on May 20, 2014).