Sparse Representation.
Computational Harmonic Analysis.
Approximation and Processing in Bases.
Time-Frequency Dictionaries.
Sparsity in Redundant Dictionaries.
Inverse Problems.
Travel Guide.
The Fourier Kingdom.
Linear Time-Invariant Filtering.
Fourier Integrals.
Properties.
Two-Dimensional Fourier Transform.
Exercises.
Discrete Revolution.
Sampling Analog Signals.
Discrete Time-Invariant Filters.
Finite Signals.
Discrete Image Processing.
Exercises.
Time Meets Frequency.
Time-Frequency Atoms.
Windowed Fourier Transform.
Wavelet Transforms.
Time-Frequency Geometry of Instantaneous Frequencies.
Quadratic Time-Frequency Energy.
Exercises.
Frames.
Frames and Riesz Bases.
Translation-Invariant Dyadic Wavelet Transform.
Subsampled Wavelet Frames.
Windowed Fourier Frames.
Multiscale Directional Frames for Images.
Exercises.
Wavelet Zoom.
Lipschitz Regularity.
Wavelet Transform Modulus Maxima.
Multiscale Edge Detection.
Multifractals.
Exercises.
Wavelet Bases.
Orthogonal Wavelet Bases.
Classes of Wavelet Bases.
Wavelets and Filter Banks.
Biorthogonal Wavelet Bases.
Wavelet Bases on an Interval.
Multiscale Interpolations.
Separable Wavelet Bases.
Lifting Wavelets.
Exercises.
Wavelet Packet and Local Cosine Base.
Wavelet Packets.
Image Wavelet Packets.
Block Transforms.
Lapped Orthogonal Transform.
Local Cosine Trees.
Exercises.
Approximations in Bases.
Linear Approximations.
Nonlinear Approximation.
Sparse Image Representations.
Exercises.
Compression.
Transform Coding.
Distortion Rate of Quantization.
High Bit Rate Compression.
Sparse Signal Compression.
Image-Compression Standards.
Exercises.
Denoising.
Estimation with Additive Noise.
Diagonal Estimation in a Basis.
Thresholding Sparse Representation.
Nondiagonal Block Thresholding.
Denoising Minimax Optimality.
Exercises.
Sparsity in Redundant Dictionaries.
Ideal Sparse Processing in Dictionaries.
Dictionaries of Orthonormal Bases.
Greedy Matching Pursuits.
L1 Pursuits.
Pursuit Recovery.
Multichannel Signals.
Leaing Dictionaries.
Exercises.
Inverse Problems.
Linear Inverse Estimation.
Thresholding Estimators for Inverse Problems.
Super-resolution.
Compressive Sensing.
Blind Source Separation.
Exercises.
APPENDIX Mathematical Complement.
Computational Harmonic Analysis.
Approximation and Processing in Bases.
Time-Frequency Dictionaries.
Sparsity in Redundant Dictionaries.
Inverse Problems.
Travel Guide.
The Fourier Kingdom.
Linear Time-Invariant Filtering.
Fourier Integrals.
Properties.
Two-Dimensional Fourier Transform.
Exercises.
Discrete Revolution.
Sampling Analog Signals.
Discrete Time-Invariant Filters.
Finite Signals.
Discrete Image Processing.
Exercises.
Time Meets Frequency.
Time-Frequency Atoms.
Windowed Fourier Transform.
Wavelet Transforms.
Time-Frequency Geometry of Instantaneous Frequencies.
Quadratic Time-Frequency Energy.
Exercises.
Frames.
Frames and Riesz Bases.
Translation-Invariant Dyadic Wavelet Transform.
Subsampled Wavelet Frames.
Windowed Fourier Frames.
Multiscale Directional Frames for Images.
Exercises.
Wavelet Zoom.
Lipschitz Regularity.
Wavelet Transform Modulus Maxima.
Multiscale Edge Detection.
Multifractals.
Exercises.
Wavelet Bases.
Orthogonal Wavelet Bases.
Classes of Wavelet Bases.
Wavelets and Filter Banks.
Biorthogonal Wavelet Bases.
Wavelet Bases on an Interval.
Multiscale Interpolations.
Separable Wavelet Bases.
Lifting Wavelets.
Exercises.
Wavelet Packet and Local Cosine Base.
Wavelet Packets.
Image Wavelet Packets.
Block Transforms.
Lapped Orthogonal Transform.
Local Cosine Trees.
Exercises.
Approximations in Bases.
Linear Approximations.
Nonlinear Approximation.
Sparse Image Representations.
Exercises.
Compression.
Transform Coding.
Distortion Rate of Quantization.
High Bit Rate Compression.
Sparse Signal Compression.
Image-Compression Standards.
Exercises.
Denoising.
Estimation with Additive Noise.
Diagonal Estimation in a Basis.
Thresholding Sparse Representation.
Nondiagonal Block Thresholding.
Denoising Minimax Optimality.
Exercises.
Sparsity in Redundant Dictionaries.
Ideal Sparse Processing in Dictionaries.
Dictionaries of Orthonormal Bases.
Greedy Matching Pursuits.
L1 Pursuits.
Pursuit Recovery.
Multichannel Signals.
Leaing Dictionaries.
Exercises.
Inverse Problems.
Linear Inverse Estimation.
Thresholding Estimators for Inverse Problems.
Super-resolution.
Compressive Sensing.
Blind Source Separation.
Exercises.
APPENDIX Mathematical Complement.