By Stephane Mallat

ISBN-10: 0123743702

ISBN-13: 9780123743701

Mallat's publication is the undisputed reference during this box - it's the just one that covers the fundamental fabric in such breadth and intensity. - Laurent Demanet, Stanford University<BR id="CRLF"><BR id="CRLF">The new version of this vintage e-book supplies all of the significant suggestions, thoughts and functions of sparse illustration, reflecting the main position the topic performs in today's sign processing. The publication basically offers the normal representations with Fourier, wavelet and time-frequency transforms, and the development of orthogonal bases with quickly algorithms. The valuable notion of sparsity is defined and utilized to sign compression, noise aid, and inverse difficulties, whereas assurance is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.<BR id="CRLF"><BR id="CRLF">Features:<BR id="CRLF"><BR id="CRLF">* Balances presentation of the maths with functions to sign processing<BR id="CRLF">* Algorithms and numerical examples are applied in WaveLab, a MATLAB toolbox<BR id="CRLF">* spouse site for teachers and chosen options and code on hand for students<BR id="CRLF"><BR id="CRLF">New during this edition<BR id="CRLF"><BR id="CRLF">* Sparse sign representations in dictionaries<BR id="CRLF">* Compressive sensing, super-resolution and resource separation<BR id="CRLF">* Geometric snapshot processing with curvelets and bandlets<BR id="CRLF">* Wavelets for special effects with lifting on surfaces<BR id="CRLF">* Time-frequency audio processing and denoising<BR id="CRLF">* snapshot compression with JPEG-2000<BR id="CRLF">* New and up-to-date exercises<BR id="CRLF"><BR id="CRLF">A Wavelet travel of sign Processing: The Sparse Way, 3rd version, is a useful source for researchers and R&D engineers wishing to use the speculation in fields comparable to picture processing, video processing and compression, bio-sensing, scientific imaging, computing device imaginative and prescient and communications engineering.<BR id="CRLF"><BR id="CRLF">Stephane Mallat is Professor in utilized arithmetic at École Polytechnique, Paris, France. From 1986 to 1996 he was once a Professor on the Courant Institute of Mathematical Sciences at ny college, and among 2001 and 2007, he co-founded and have become CEO of a picture processing semiconductor company.<BR id="CRLF"><BR id="CRLF">Companion website: A Numerical journey of sign Processing

* contains the entire newest advancements because the publication was once released in 1999, together with its<BR id="CRLF">application to JPEG 2000 and MPEG-4<BR id="CRLF">* Algorithms and numerical examples are carried out in Wavelab, a MATLAB toolbox<BR id="CRLF">* Balances presentation of the maths with functions to sign processing

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Extra info for A Wavelet Tour of Signal Processing: The Sparse Way (3rd Edition)

Example text

Images with piecewise regular edges have representations that are asymptotically more sparse by thresholding curvelet coefficients than wavelet coefficients. 2 Ideal Dictionary Approximations In a redundant dictionary D ϭ {␾p }p∈⌫ , we would like to find the best approximation support ⌳ with M ϭ |⌳| vectors, which minimize the error f Ϫ f⌳ 2 . 16) for some multiplier T . Compression and denoising are two applications of redundant dictionary approximations. 16),with a multiplier T that depends on the quantization step.

This is equivalent to approximating the derivative by a finite difference on an interval h that goes to zero: f V ϭ lim ϩϱ h→0 Ϫϱ | f (t) Ϫ f (t Ϫ h)| dt. 58) The total variation of discontinuous functions is thus well defined. 58) gives f V ϭ 2. We say that f has a bounded variation if f V Ͻ ϩϱ. 3 Properties Whether f Ј is the standard derivative of f or its generalized derivative in the sense of distributions, its Fourier transform is f Ј(␻) ϭ i␻fˆ (␻). Therefore |␻| | fˆ (␻)| р ϩϱ Ϫϱ | f Ј(t)|dt ϭ f V, which implies that | fˆ (␻)| р f V .

The book begins with Chapters 2 and 3, which review the Fourier transform and linear discrete signal processing. They provide the necessary background for readers with no signal-processing background. Important properties of linear operators, projectors, and vector spaces can be found in the Appendix. Local timefrequency transforms and dictionaries are presented in Chapter 4; the wavelet and windowed Fourier transforms are introduced and compared. The measurement of instantaneous frequencies illustrates the limitations of time-frequency resolution.

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