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 UniversityThe new edition of this classic book gives all the major concepts, techniques and applications of sparse representatio...
| Autor principal: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Elsevier /Academic Press
c2009.
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| Edición: | Sparse ed |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009627486106719 |
Tabla de Contenidos:
- Front 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
- 1.4 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
- 2.3.2 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
- 3.4.2 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
- 4.5.2 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 à Trous; 5.3 Subsampled Wavelet Frames; 5.4 Windowed Fourier Frames; 5.4.1 Tight Frames; 5.4.2 General Frames
- 5.5 Multiscale Directional Frames For Images
