A Wavelet Tour of Signal Processing: The Sparse Way
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University
The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.
* Balances presentation of the mathematics with applications to signal processing
* Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox
New in this edition
* Sparse signal representations in dictionaries
* Compressive sensing, super-resolution and source separation
* Geometric image processing with curvelets and bandlets
* Wavelets for computer graphics with lifting on surfaces
* Time-frequency audio processing and denoising
* Image compression with JPEG-2000
* New and updated exercises
A Wavelet Tour of Signal Processing: The Sparse Way, Third Edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.
Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company.
application to JPEG 2000 and MPEG-4
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Chapter 9 Approximations in Bases
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algorithm amplitude approximation error bandlet basis pursuit biorthogonal wavelet block thresholding bounded variation calculated compact support compression computed conjugate mirror filters constructed convergence convolution corresponding cosine basis curvelet Daubechies decay decomposed defined denoising derive diagonal Dirac discrete signal distortion rate distribution dyadic wavelet edges energy fB[m Figure filter bank finite Gabor Gabor atoms Gaussian implemented implies inner product interpolation intervals inverse iterations Lagrangian linear approximation log2 loge matching pursuit minimax minimization modulus maxima nonlinear approximation nonzero norm obtained operator optimal orthogonal basis orthogonal projection orthonormal basis packet basis polynomial projector Proof proves quantization random reconstruction recovered redundant resulting Riesz basis sampling satisfies scale 2j scaling functions Section shows signal f singular space spline super-resolution Theorem thresholding estimator time-frequency transform code translation-invariant uniformly Lipschitz vanishing moments verify wavelet basis wavelet coefficients wavelet packet bases wavelet transform Wigner-Ville distribution zero