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Licensed Unlicensed Requires Authentication Published by Princeton University Press 2006

Orthonormal Bases of Compactly Supported Wavelets

From the book Fundamental Papers in Wavelet Theory

  • Ingrid Daubechles
https://doi.org/10.1515/9781400827268.564
From the book
Fundamental Papers in Wavelet Theory
Fundamental Papers in Wavelet Theory

Chapters in this book (51)

Frontmatter
Contents
Contributor Affiliations
Preface
Foreword
Introduction
Section I. Precursors in Signal Processing
Introduction
The Laplacian Pyramid as a Compact Image Code
Digital Coding of Speech in Sub-bands
Application of quadrature mirror filters to split-band voice coding schemes
Procedure for designing exact reconstruction filter banks for tree-structured subband coders
Filters for distortion-free two-band multirate filter banks
Filter banks allowing perfect reconstruction
Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property
SECTION II. Precursors in Physics: Affine Coherent States
Introduction
Continuous representation theory using the affine group
Decomposition of Hardy functions into square integrable wavelets of constant shape
Transforms associated to square integrable group representations I General results
Section III. Precursors in Mathematics: Early Wavelet Bases
Introduction
On the Theory of Orthogonal Function Systems
A set of continuous orthogonal functions
A modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy spaces
Uncertainty Principle, Hilbert Bases and Algebras of Operators
Wavelets and Hilbert Bases
A block spin construction of Ondelettes. Part i: Lemarié Functions
SECTION IV. Precursors and Development in Mathematics: Atom and Frame Decompositions
Introduction
A Class of Nonharmonic Fourier Series
Extensions of Hardy Spaces and Their Use in Analysis
Painless Nonorthogonal Expansions
Decomposition of Besov Spaces
Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions, I
The Wavelet Transform, Time-Frequency Localization And Signal Analysis
Section V. Multiresolution Analysis
Introduction
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
Wavelets with Compact Support
Approximations and Wavelet Orthonormal Bases of L<Sup>2</Sup>(R)
Wavelets, Multiresolution Analysis, and Quadrature Mirror F
Tight frames of compactly supported affine wavelets
Orthonormal Bases of Compactly Supported Wavelets
SECTION VI. Multidimensional Wavelets
Introduction
Wavelets, Spline Functions, and Multiresolution Analysis
Multiscale Analyses and Wavelet Bases
Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn
Multiresolution analysis, Haar bases and self-similar tilings of Rn
SECTION VII. Selected Applications
Introduction
Fast wavelet transforms and numerical algorithms
Compression of wavelet decompositions
Adapting to unknown smoothness by wavelet shrinkage
Hölder Exponents at Given Points and Wavelet Coefficients
Embedded image coding using zerotrees of wavelet coefficients
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