| preface to the sparse edition . notations chapter 1 sparse representations 1.1 computational harmonic analysis 1.2 approximation and processing in bases 1.3 time-frequency dictionaries 1.4 sparsity in redundant dictionaries 1.5 inverse problems 1.6 travel guide chapter 2 the fourier kingdom 2.1 linear time-lnvariant filtering 2.2 fourier integrals 2.3 properties 2.4 two-dimensional fourier transform 2.5 exercises chapter 3 discrete revolution 3.1 sampling analog signals 3.2 discrete time-invariant filters 3.3 finite signals 3.4 discrete image processing .3.5 exercises chapter 4 time meets frequency 4.1 time-frequency atoms 4.2 windowed fourier transform 4.3 wavelet transforms 4.4 time-frequency geometry of instantaneous frequencies 4.5 quadratic time-frequency energy 4.6 exercises chapter 5 frames 5.1 frames and riesz bases 5.2 translation-invariant dyadic wavelet transform 5.3 subsampled wavelet frames 5.4 windowed fourier frames 5.5 multiscale directional frames for images 5.6 exercises chapter 6 wavelet zoom 6.1 lipschitz regularity 6.2 wavelet transform modulus maxima 6.3 multiscale edge detection 6.4 multifractals 6.5 exercises chapter 7 wavelet bases 7.1 orthogonal wavelet bases 7.2 classes of wavelet bases 7.3 wavelets and filter banks 7.4 biorthogonal wavelet bases 7.5 wavelet bases on an interval 7.6 multiscale interpolations 7.7 separable wavelet bases 7.8 lifting wavelets 7.9 exercises chapter 8 wavelet packet and local cosine bases 8.1 wavelet packets 8.2 image wavelet packets 8.3 block transforms 8.4 lapped orthogonal transforms 8.5 local cosine trees 8.6 exercises chapter 9 approximations in bases .. 9.1 linear approximations 9.2 nonlinear approximations 9.3 sparse image representations 9.4 exercises chapter 10 compression 10.1 transform coding 10.2 distortion rate of quantization 10.3 high bit rate compression 10.4 sparse signal compression 10.5 image-compression standards 10.6 exercises chapter 11 denoising 11.1 estimation with additive noise 11.2 diagonal estimation in a basis 11.3 thresholding sparse representations 11.4 nondiagonal blockthresholding 11.5 denoising minimax optimality 11.6 exercises chapter 12 sparsity in redundant dictionaries 12.1 ideal sparse processing in dictionaries 12.2 dictionaries of orthonormal bases 12.3 greedy matching pursuits 12.4 11 pursuits 12.5 pursuit recovery 12.6 multichannel signals 12.7 learning dictionaries 12.8 exercises chapter 13 inverse problems 13.1 linear inverse estimation 13.2 thresholding estimators for inverse problems 13.3 super-resolution 13.4 compressive sensing 13.5 blind source separation 13.6 exercises appendix mathematical complements bibliography index ... |
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