LEADER 05891nam 2200721Ia 450 001 9910824696403321 005 20220307194308.0 010 $a1-281-98216-4 010 $a9786611982164 010 $a0-08-092202-3 035 $a(CKB)1000000000702851 035 $a(EBL)413871 035 $a(OCoLC)437092007 035 $a(SSID)ssj0000269437 035 $a(PQKBManifestationID)11192808 035 $a(PQKBTitleCode)TC0000269437 035 $a(PQKBWorkID)10243050 035 $a(PQKB)11596488 035 $a(Au-PeEL)EBL413871 035 $a(CaPaEBR)ebr10276390 035 $a(CaONFJC)MIL198216 035 $a(PPN)184032725 035 $a(OCoLC)795224966 035 $a(OCoLC)ocn795224966 035 $a(FR-PaCSA)88812130 035 $a(CaSebORM)9780123743701 035 $a(MiAaPQ)EBC413871 035 $a(EXLCZ)991000000000702851 100 $a20080926d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA wavelet tour of signal processing $ethe Sparse way /$fStephane Mallat 205 $aSparse ed. 210 $aAmsterdam ;$aBoston $cElsevier /Academic Press$dc2009 215 $a1 online resource (829 p.) 300 $a"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." 311 $a0-12-374370-2 320 $aIncludes bibliographical references (p. 765-793) and index. 327 $aFront Cover; A Wavelet Tour of Signal Processing; Copyright Page; Dedication Page; Table of Contents; Preface to the Sparse Edition; Notations; Chapter 1. Sparse Representations; 1.1 Computational Harmonic Analysis; 1.1.1 The Fourier Kingdom; 1.1.2 Wavelet Bases; 1.2 Approximation and Processing in Bases; 1.2.1 Sampling with Linear Approximations; 1.2.2 Sparse Nonlinear Approximations; 1.2.3 Compression; 1.2.4 Denoising; 1.3 Time-Frequency Dictionaries; 1.3.1 Heisenberg Uncertainty; 1.3.2 Windowed Fourier Transform; 1.3.3 Continuous Wavelet Transform; 1.3.4 Time-Frequency Orthonormal Bases 327 $a1.4 Sparsity in Redundant Dictionaries1.4.1 Frame Analysis and Synthesis; 1.4.2 Ideal Dictionary Approximations; 1.4.3 Pursuit in Dictionaries; 1.5 Inverse Problems; 1.5.1 Diagonal Inverse Estimation; 1.5.2 Super-resolution and Compressive Sensing; 1.6 Travel Guide; 1.6.1 Reproducible Computational Science; 1.6.2 Book Road Map; Chapter 2. The Fourier Kingdom; 2.1 Linear Time-Invariant Filtering; 2.1.1 Impulse Response; 2.1.2 Transfer Functions; 2.2 Fourier Integrals; 2.2.1 Fourier Transform in L1(R); 2.2.2 Fourier Transform in L2(R); 2.2.3 Examples; 2.3 Properties; 2.3.1 Regularity and Decay 327 $a2.3.2 Uncertainty Principle2.3.3 Total Variation; 2.4 Two-Dimensional Fourier Transform; 2.5 Exercises; Chapter 3. Discrete Revolution; 3.1 Sampling Analog Signals; 3.1.1 Shannon-Whittaker Sampling Theorem; 3.1.2 Aliasing; 3.1.3 General Sampling and Linear Analog Conversions; 3.2 Discrete Time-Invariant Filters; 3.2.1 Impulse Response and Transfer Function; 3.2.2 Fourier Series; 3.3 Finite Signals; 3.3.1 Circular Convolutions; 3.3.2 Discrete Fourier Transform; 3.3.3 Fast Fourier Transform; 3.3.4 Fast Convolutions; 3.4 Discrete Image Processing; 3.4.1 Two-Dimensional Sampling Theorems 327 $a3.4.2 Discrete Image Filtering3.4.3 Circular Convolutions and Fourier Basis; 3.5 Exercises; Chapter 4. Time Meets Frequency; 4.1 Time-Frequency Atoms; 4.2 Windowed Fourier Transform; 4.2.1 Completeness and Stability; 4.2.2 Choice of Window; 4.2.3 Discrete Windowed Fourier Transform; 4.3 Wavelet Transforms; 4.3.1 Real Wavelets; 4.3.2 Analytic Wavelets; 4.3.3 Discrete Wavelets; 4.4 Time-Frequency Geometry of Instantaneous Frequencies; 4.4.1 Analytic Instantaneous Frequency; 4.4.2 Windowed Fourier Ridges; 4.4.3 Wavelet Ridges; 4.5 Quadratic Time-Frequency Energy; 4.5.1 Wigner-Ville Distribution 327 $a4.5.2 Interferences and Positivity4.5.3 Cohen's Class; 4.5.4 Discrete Wigner-Ville Computations; 4.6 Exercises; Chapter 5. Frames; 5.1 Frames and Riesz Bases; 5.1.1 Stable Analysis and Synthesis Operators; 5.1.2 Dual Frame and Pseudo Inverse; 5.1.3 Dual-Frame Analysis and Synthesis Computations; 5.1.4 Frame Projector and Reproducing Kernel; 5.1.5 Translation-Invariant Frames; 5.2 Translation-Invariant Dyadic Wavelet Transform; 5.2.1 Dyadic Wavelet Design; 5.2.2 Algorithme a? Trous; 5.3 Subsampled Wavelet Frames; 5.4 Windowed Fourier Frames; 5.4.1 Tight Frames; 5.4.2 General Frames 327 $a5.5 Multiscale Directional Frames For Images 330 $aMallat'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 UniversityThe 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 explaine 606 $aSignal processing$xMathematics 606 $aWavelets (Mathematics) 615 0$aSignal processing$xMathematics. 615 0$aWavelets (Mathematics) 676 $a621.382/2015152433 676 $a621.3822015152433 676 $a621.3822015152433 700 $aMallat$b S. G$g(Ste?phane G.)$0340541 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910824696403321 996 $aWavelet Tour of Signal Processing$9134628 997 $aUNINA