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Sparse Image and Signal Processing, Second Edition

Book Description

This thoroughly updated new edition presents state of the art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB® and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.

Table of Contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Table of Contents
  6. List of Acronyms
  7. Notation
  8. Foreword
  9. 1 Introduction to the World of Sparsity
    1. 1.1 Sparse Representation
    2. 1.2 From Fourier to Wavelets
    3. 1.3 From Wavelets to Overcomplete Representations
    4. 1.4 Novel Applications of the Wavelet and Curvelet Transforms
    5. 1.5 Summary
  10. 2 The Wavelet Transform
    1. 2.1 Introduction
    2. 2.2 The Continuous Wavelet Transform
    3. 2.3 Examples of Wavelet Functions
    4. 2.4 Continuous Wavelet Transform Algorithm
    5. 2.5 The Discrete Wavelet Transform
    6. 2.6 Nondyadic Resolution Factor
    7. 2.7 The Lifting Scheme
    8. 2.8 Wavelet Packets
    9. 2.9 Guided Numerical Experiments
    10. 2.10 Summary
  11. 3 Redundant Wavelet Transform
    1. 3.1 Introduction
    2. 3.2 The Undecimated Wavelet Transform
    3. 3.3 Partially Decimated Wavelet Transform
    4. 3.4 The Dual-Tree Complex Wavelet Transform
    5. 3.5 Isotropic Undecimated Wavelet Transform: Starlet Transform
    6. 3.6 Nonorthogonal Filter Bank Design
    7. 3.7 Pyramidal Wavelet Transform
    8. 3.8 Guided Numerical Experiments
    9. 3.9 Summary
  12. 4 Nonlinear Multiscale Transforms
    1. 4.1 Introduction
    2. 4.2 Decimated Nonlinear Transform
    3. 4.3 Multiscale Transform and Mathematical Morphology
    4. 4.4 Multiresolution Based on the Median Transform
    5. 4.5 Guided Numerical Experiments
    6. 4.6 Summary
  13. 5 Multiscale Geometric Transforms
    1. 5.1 Introduction
    2. 5.2 Background and Example
    3. 5.3 Ridgelets
    4. 5.4 Curvelets
    5. 5.5 Curvelets and Contrast Enhancement
    6. 5.6 Guided Numerical Experiments
    7. 5.7 Summary
  14. 6 Sparsity and Noise Removal
    1. 6.1 Introduction
    2. 6.2 Term-by-Term Nonlinear Denoising
    3. 6.3 Block Nonlinear Denoising
    4. 6.4 Beyond Additive Gaussian Noise
    5. 6.5 Poisson Noise and the Haar Transform
    6. 6.6 Poisson Noise with Low Counts
    7. 6.7 Guided Numerical Experiments
    8. 6.8 Summary
  15. 7 Linear Inverse Problems
    1. 7.1 Introduction
    2. 7.2 Sparsity-Regularized Linear Inverse Problems
    3. 7.3 Basics of Convex Analysis and Proximal Calculus
    4. 7.4 Proximal Splitting Framework
    5. 7.5 Selected Problems and Algorithms
    6. 7.6 Non-Convex Problems
    7. 7.7 General Discussion: Sparsity, Inverse Problems, and Iterative Thresholding
    8. 7.8 Guided Numerical Experiments
    9. 7.9 Summary
  16. 8 Morphological Diversity
    1. 8.1 Introduction
    2. 8.2 Dictionary and Fast Transformation
    3. 8.3 Combined Denoising
    4. 8.4 Combined Deconvolution
    5. 8.5 Morphological Component Analysis
    6. 8.6 Texture-Cartoon Separation
    7. 8.7 Inpainting
    8. 8.8 Guided Numerical Experiments
    9. 8.9 Summary
  17. 9 Sparse Blind Source Separation
    1. 9.1 Introduction
    2. 9.2 Independent Component Analysis
    3. 9.3 Sparsity and Multichannel Data
    4. 9.4 Morphological Diversity and Blind Source Separation
    5. 9.5 Non-Negative Matrix Factorization
    6. 9.6 Guided Numerical Experiments
    7. 9.7 Summary
  18. 10 Dictionary Learning
    1. 10.1 Introduction
    2. 10.2 Dictionary Learning Strategy
    3. 10.3 Dictionary Learning and Linear Inverse Problems
    4. 10.4 Guided Numerical Experiments
    5. 10.5 Summary
  19. 11 Three-Dimensional Sparse Representations
    1. 11.1 Introduction
    2. 11.2 3-D Wavelets
    3. 11.3 3-D Ridgelets and Beamlets
    4. 11.4 First-Generation 3-D Curvelets
    5. 11.5 Fast Curvelets
  20. 12 Multiscale Geometric Analysis on the Sphere
    1. 12.1 Introduction
    2. 12.2 Data on the Sphere
    3. 12.3 Orthogonal Haar Wavelets on the Sphere
    4. 12.4 Continuous Wavelets on the Sphere
    5. 12.5 Redundant Wavelet Transform on the Sphere with Exact Reconstruction
    6. 12.6 Curvelet Transform on the Sphere
    7. 12.7 Restoration and Decomposition on the Sphere
    8. 12.8 2-D–1-D Wavelet on the Sphere
    9. 12.9 Three-Dimensional Wavelets on the Ball
    10. 12.10 Applications
    11. 12.11 Guided Numerical Experiments
    12. 12.12 Summary
  21. 13 Compressed Sensing
    1. 13.1 Introduction
    2. 13.2 The Sensing Protocol
    3. 13.3 RIP-approach of Compressed Sensing
    4. 13.4 RIP-less Compressed Sensing
    5. 13.5 Compressed Sensing in Space Science
    6. 13.6 Guided Numerical Experiments
    7. 13.7 Summary
  22. 14 This Book’s Take-Home Message
  23. Notes
  24. References
  25. Index