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Sparse Representation, Modeling and Learning in Visual Recognition: Theory, Algorithms and Applications.

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Bibliographic Details
Authors and Corporations: Cheng, Hong
Edition: 1st ed.
Type of Resource: E-Book
Language: English
published:
London : Springer London, Limited, 2015.
©2015.
Series: Advances in Computer Vision and Pattern Recognition Series
Subjects:
Computer vision.
Electronic books.
Source: Ebook Central
ISBN: 9781447167143
Table of Contents:
  • Intro
  • Preface
  • Contents
  • Mathematical Notation
  • Part I Introduction and Fundamentals
  • 1 Introduction
  • 1.1 Sparse Representation, Modeling, and Learning
  • 1.1.1 Sparse Representation
  • 1.1.2 Sparse Modeling
  • 1.1.3 Sparse Learning
  • 1.2 Visual Recognition
  • 1.2.1 Feature Representation and Learning
  • 1.2.2 Distance Metric Learning
  • 1.2.3 Classification
  • 1.3 Other Applications
  • 1.3.1 Single-Pixel Cameras
  • 1.3.2 Superresolution
  • References
  • 2 The Fundamentals of Compressed Sensing
  • 2.1 Sampling Theorems
  • 2.2 Compressive Sampling
  • 2.2.1 Random Projection and Measurement Matrix
  • 2.2.2 Sparsity
  • 2.2.3 Structured Sparsity
  • 2.3 ell0, ell1 and ell2 Norms
  • 2.4 Spark and Singleton Bound
  • 2.5 Null Space Property
  • 2.6 Uniform Uncertainty Principle, Incoherence Condition
  • 2.7 ell1 and ell0 Equivalence
  • 2.8 Stable Recovery Property
  • 2.9 Information Theory
  • 2.9.1 K-sparse Signal Model
  • 2.9.2 The Entropy of K-sparse Signals
  • 2.9.3 Mutual Information
  • 2.10 Sparse Convex Optimization
  • 2.10.1 Introduction to Convex Optimization
  • 2.10.2 Gradient, Subgradient, Accelerated Gradient
  • 2.10.3 Augmented Lagrangian Method
  • References
  • Part II Sparse Representation, Modeling and Learning
  • 3 Sparse Recovery Approaches
  • 3.1 Introduction
  • 3.2 Convex Relaxation
  • 3.2.1 Linear Programming Solutions
  • 3.2.2 Second-Order Cone Programs with Log-Barrier Method
  • 3.2.3 ell1-Homotopy Methods
  • 3.2.4 Elastic Net
  • 3.3 Greedy Algorithms
  • 3.3.1 MP and OMP
  • 3.3.2 CoSaMP
  • 3.3.3 Iterative Hard Thresholding Algorithm
  • 3.4 Sparse Bayesian Learning
  • 3.4.1 Bayesian Viewpoint of Sparse Representation
  • 3.4.2 Sparse Representation via Relevance Vector Machine
  • 3.4.3 Sparse Bayesian Learning
  • 3.5 ell0-Norm Gradient Minimization
  • 3.5.1 Counting Gradient Difference.
  • 3.5.2 ell0-Norm Sparse Optimization Problems
  • 3.5.3 ell0-Norm Sparse Solution
  • 3.5.4 Applications
  • 3.6 The Sparse Feature Projection Approach
  • 3.6.1 Gaussian Process Regression for Feature Transforms
  • 3.6.2 Sparse Projection of Input Feature Vectors
  • References
  • 4 Robust Sparse Representation, Modeling and Learning
  • 4.1 Introduction
  • 4.2 Robust Statistics
  • 4.2.1 Connection Between MLE and Residuals
  • 4.2.2 M-Estimators
  • 4.3 Robust Sparse PCA
  • 4.3.1 Introduction
  • 4.3.2 PCA
  • 4.3.3 Robust Sparse Coding
  • 4.3.4 Robust SPCA
  • 4.3.5 Applications
  • References
  • 5 Efficient Sparse Representation and Modeling
  • 5.1 Introduction
  • 5.1.1 Large-Scale Signal Representation and Modeling
  • 5.1.2 The Computation Complexity of Different Sparse Recovery Algorithms
  • 5.2 The Feature-Sign Search Algorithms
  • 5.2.1 Fixed-Point Continuations for ell1-minimization
  • 5.2.2 The Basic Feature-Sign Search Algorithm
  • 5.2.3 The Subspace Shrinkage and Optimization Algorithm
  • 5.3 Efficient Sparse Coding Using Graphical Models
  • 5.3.1 Graphical Models of CS Encoding Matrix
  • 5.3.2 Bayesian Compressive Sensing
  • 5.3.3 Bayesian Compressive Sensing Using Belief Propagation (CS-BP)
  • 5.4 Efficient Sparse Bayesian Learning
  • 5.4.1 Introduction
  • 5.4.2 Sequential Sparse Bayesian Models
  • 5.4.3 The Algorithm Flowchart
  • 5.5 Sparse Quantization
  • 5.5.1 Signal Sparse Approximation Problems
  • 5.5.2 K-Highest Sparse Quantization
  • 5.6 Hashed Sparse Representation
  • 5.6.1 Hash Functions
  • 5.6.2 Structured Dictionary Learning
  • 5.6.3 Hashing and Dictionary Learning
  • 5.6.4 Flowchart of Algorithm
  • 5.7 Compressive Feature
  • 5.7.1 Generating Compressive
  • 5.7.2 Applications
  • References
  • Part III Visual Recognition Applications
  • 6 Feature Representation and Learning
  • 6.1 Introduction
  • 6.2 Feature Extraction.
  • 6.2.1 Feature Representation Using Sparse Coding
  • 6.2.2 Feature Coding and Pooling
  • 6.2.3 Invariant Features
  • 6.3 Dictionary Learning
  • 6.3.1 K-SVD
  • 6.3.2 Discriminative Dictionary Learning
  • 6.3.3 Online Dictionary Learning
  • 6.3.4 Supervised Dictionary Learning
  • 6.3.5 Joint Dictionary Learning and Other Tasks
  • 6.3.6 Applications
  • -Image/Video Restoration
  • 6.4 Feature Learning
  • 6.4.1 Dimensionality Reduction
  • 6.4.2 Sparse Support Vector Machines
  • 6.4.3 Recursive Feature Elimination
  • 6.4.4 Minimum Squared Error (MSE) Criterions
  • 6.4.5 Elastic Net Criterions
  • 6.4.6 Sparse Linear Discriminant Analysis
  • 6.4.7 Saliency Feature Mapping Using Sparse Coding
  • References
  • 7 Sparsity-Induced Similarity
  • 7.1 Introduction
  • 7.2 Sparsity-Induced Similarity
  • 7.2.1 The Clustering Condition of Subspaces
  • 7.2.2 The Sparse-Induced Similarity Measure
  • 7.2.3 Nonnegative Sparsity-Induced Similarity
  • 7.2.4 Some Basic Issues in SIS
  • 7.2.5 A Toy Problem
  • 7.3 Application
  • 7.3.1 Label Propagation
  • 7.3.2 Human Activity Recognition
  • 7.3.3 Visual Tracking
  • 7.3.4 Image Categorization
  • 7.3.5 Spam Image Cluster
  • References
  • 8 Sparse Representation and Learning-Based Classifiers
  • 8.1 Introduction
  • 8.2 Sparse Representation-Based Classifiers (SRC)
  • 8.2.1 The SRC Algorithm and Its Invariants
  • 8.2.2 Classification Error Analysis
  • 8.3 Sparse Coding-Based Spatial Pyramid Matching (ScSPM)
  • 8.3.1 Assignment-Based Sparse Coding
  • 8.3.2 The Spatial Pooling
  • 8.3.3 The Sparse Coding-Based Spatial Pyramid Matching
  • 8.4 Sparsity Coding-Based Nearest Neighbor Classifiers (ScNNC)
  • 8.4.1 Sparse Coding-Based Naive Bayes Nearest Neighbor
  • 8.4.2 Sparse Approximated Nearest Points (SANP) Approaches
  • 8.5 Sparse Coding-Based Deformable Part Models (ScDPM)
  • 8.5.1 Deformable Part Models
  • 8.5.2 Sparselet Models.
  • 8.5.3 The Flowchart of ScDPM
  • References
  • Part IV Advanced Topics
  • 9 Beyond Sparsity
  • 9.1 Low-Rank Matrix Approximation
  • 9.1.1 Introduction
  • 9.1.2 ell2-norm Wiberg Algorithm
  • 9.1.3 ell1-norm Wiberg Algorithm
  • 9.2 Graphical Models in Compressed Sensing
  • 9.2.1 Inference via Message Passing Algorithm
  • 9.2.2 Inference via Approximate Message Passing Algorithm
  • 9.3 Collaborative Representation-Based Classifiers
  • 9.3.1 Sparse Representation and Collaborative Representation
  • 9.3.2 Collaborative Representation-Based Classification (CRC)
  • 9.4 High-Dimensional Nonlinear Learning
  • 9.4.1 Kernel Sparse Representation
  • 9.4.2 Anchor Points Approaches
  • 9.4.3 Sparse Manifold Learning
  • References
  • Appendix A Mathematics
  • Appendix B Computer Programming Resourcesfor Sparse Recovery Approaches
  • Appendix C The Source Code of Sparsity InducedSimilarity
  • Appendix DDerivations
  • Index.