Wavelets
Theory and Applications
1st Edition
Published in December 1996
523 pages
978-0-19-802542-9 (ISBN)
Description
Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small `window'. They are used to magnify experimental or numerical data and have become powerful tools in signal processing, image processing, and other fields of computational sciences. This book is a collection of chapters written by the five lecturers of a short course co-sponsored by the Institute of Computer Applications in Science and Engineering (ICASE).
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04/1996
Oxford University Press Inc
€308.40
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Content
- Intro
- Contents
- Preface
- 1 Introduction to Wavelets and their Application to Partial Differential Equations
- 1 Introduction and Motivation
- 2 Definition of Daubechies-Based Wavelets
- 3 Restriction to Finite Dimensions
- 4 Analysis and Data Compression
- 5 Daubechies Wavelets and CFD
- 6 The Wavelet-Optimized Finite Difference Method
- 7 Collocation Methods
- 8 Harten's Multiresolution Method
- 9 Spline Wavelets and CFD
- 10 Wavelets Compared to Other Methods
- 11 References
- 2 Wavelets from Filter Banks
- 1 Introduction
- 2 The Idea of Multiresolution
- 3 Wavelets From Filters
- 4 Dilation Equation: Time Domain
- 5 Dilation Equation: Frequency Domain
- 6 References
- 3 Wavelets, Functions, and Operators
- 1 Introduction: The Origin of Wavelets in Mathematics
- 2 Basic Concepts
- 3 The Modulus of the Coefficients
- 4 The Phase of the Coefficients
- 5 Multiresolution Analysis and Wavelet Bases
- 6 Operators
- 7 Calderón-Zygmund Operators and Characterization of Functional Spaces
- 8 Calderón-Zygmund Operators, Matrices and Functional Calculus
- 9 Adapting the Wavelets
- 10 References
- 4 Wavelets, Multiresolution Analysis and Fast Numerical Algorithms
- 1 Introduction
- 2 Preliminary Remarks
- 3 The Non-Standard and Standard Forms
- 4 Compression of Operators
- 5 Differential Operators in Wavelet Bases
- 6 Convolution Operators in Wavelet Bases
- 7 The Two-Point Boundary Value Problem
- 8 Multiplication of Operators
- 9 Fast Iterative Algorithms in Wavelet Bases
- 10 Product of Functions in Wavelet Bases
- 11 References
- 5 Some Wavelet Algorithms for Partial Differential Equations
- 1 Introduction
- 2 Approximation of Functions
- 3 Fast Algorithms
- 4 Differential Operators
- 5 Approximation of Elliptic Operators
- 6 Adaptive Algorithms
- 7 Numerical Implementation
- 8 Conclusion
- 9 References
- 6 Some Wavelet Algorithms for Turbulence Analysis and Modeling
- 1 Introduction
- 2 Analysis Algorithms of the Wavelet Plane
- 3 Application to Transition and Turbulence
- 4 Conclusion
- 5 References
- 7 Wavelet Analysis of Fractals: from the Mathematical Concepts to Experimental Reality
- 1 Introduction
- 2 The Multifractal Formalism
- 3 Singularity Detection and Processing with Wavelets
- 4 A Multifractal Formalism for Distributions Based on Wavelets
- 5 Numerical and Experimental Applications of the Wavelet Transform Modulus Maxima Method
- 6 Wavelet Analysis of Fully-Developed Turbulence Data
- 7 Wavelet Analysis of Fractal Growth Phenomena
- 8 Prospects: Solution to the Inverse Fractal Problem from Wavelet Analysis
- 9 References
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
