UID:
almafu_9960074047402883
Format:
1 online resource (656 p.)
ISBN:
0-12-174575-9
,
1-322-46547-9
Series Statement:
Waveletss Analysis and its Application ; Volume 5
Content:
Wavelets: Theory, Algorithms, and Applications is the fifth volume in the highly respected series, WAVELET ANALYSIS AND ITS APPLICATIONS. This volume shows why wavelet analysis has become a tool of choice infields ranging from image compression, to signal detection and analysis in electrical engineering and geophysics, to analysis of turbulent or intermittent processes. The 28 papers comprising this volume are organized into seven subject areas: multiresolution analysis, wavelet transforms, tools for time-frequency analysis, wavelets and fractals, numerical methods and algorithms, and applicat
Note:
Description based upon print version of record.
,
Front Cover; Wavelets: Theory, Algorithms, and Applications; Copyright Page; Table of Contents; Contributors; Preface; Part I: Multiresolution and Multilevel Analyses; Chapter 1. Non-stationary Multiscale Analysis; 1 Introduction; 2 Regularity and time-frequency localization in the standard case; 3 Non-stationary wavelets; 4 Non-stationary wavelet packets; References; Chapetr 2. The Spectral Theory of Multiresolution Operators and Applications; 1 Introduction; 2 Wavelets and multiresolution operators; 3 The Lawton-Cohen-Gopinath Theorem on wavelet orthonormal bases
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4 Differentiability estimates via the spectral theory of the multiresolution operator5 Conclusion; References; Chapter 3. Multiresolution Analysis, Haar Bases and Wavelets on Riemannian Manifolds; 1 Introduction; 2 Construction of a multiresolution analysis; 3 Construction of a generalized Haar function; 4 Examples; 5 Wavelets; References; Chapter 4. Orthonormal Cardinal Functions; 1 Introduction; 2 Local orthogonal spline projectors with a given accuracy; 3 Orthonormal cardinal functions using cardinal splines; 4 Orthonormal refinable cardinal functions; References
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Part II: Wavelet TransformsChapter 5. Some Remarks on Wavelet Representations and Geometric Aspects; 1 Introduction; 2 The group-theoretical picture; 3 Examples; 4 Algorithms from group theoretical considerations; 5 Approximate algorithms; References; Chapter 6. A Matrix Approach to Discrete Wavelets; 1 Introduction; 2 Towards matrices; 3 Factorizations of compactly supported orthogonal wavelets; 4 Biorthogonal wavelet transforms; 5 Vanishing moments and regularity of wavelet matrices; 6 Construction from the first row; 7 Symmetric orthogonal wavelets; References
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Chapter 7. A Unified Approach to Periodic Wavelets1 Introduction; 2 Periodic shift-invariant spaces; 3 Periodic multiresolution; 4 Periodic wavelet spaces; 5 Decomposition and reconstruction algorithms; References; Part III: Spline Wavelets; Chapter 8. Spline Wavelets over R, Z, R/NZ, and Z/NZ; 1 Introduction; 2 Generalized cardinal B-splines over classical LCA groups; 3 Generalized Euler-Frobenius polynomials; 4 Multiresolution analysis; 5 Shifted spline wavelets; 6 Decomposition and reconstruction of functions; References
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Chapter 9. A Practice of Data Smoothing by B-spline Wavelets1 Introduction; 2 Compactly supported B-spline wavelets; 3 The cubic cardinal B-spline wavelet analysis; 4 An application to mechanical vibration; 5 Conclusion; References; Chapter 10. L-Spline Wavelets; 1 Introduction; 2 L-splines; 3 A basis of locally supported splines; 4 L-spline wavelets; 5 The translation invariant case; 6 A multiresolution framework; 7 Examples; References; Chapter 11. Wavelets and Frames on the Four-Directional Mesh; 1 Introduction; 2 Four-directional box splines as scaling functions
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3 Four-directional wavelets
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English
Additional Edition:
ISBN 1-4933-0739-8
Additional Edition:
ISBN 0-08-052084-7
Language:
English
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