Fundamental Papers in Wavelet Theory / / Christopher Heil, David F. Walnut.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Heil, Christopher,; Walnut, David F.,
• MitwirkendeR: ADELSON, EDWARD H.,; Antoine, Jean-Pierre,; Barnwell, T. P.,; Battle, Guy,; Benedetto, John J.,; Beylkin, G.,; Burt, Peter J.,; Cohen, A.,; Coifman, R.,; Coifman, Ronald R.,; Crochiere, R. E.,; Daubechies, Ingrid,; Daubechles, Ingrid,; DeVore, Ronald A.,; Donoho, David L.,; Esteban, D.,; Feichtinger, Hans G.,; Flanagan, J . L.,; Franklin, Philip,; Frazier, Michael,; Galand, C.,; Grossmann, A.,; Gröchenig, K. H.,; Gröchenig, K.,; Gröchenig, Karlheinz,; Haar, Alfred,; Heil, Christopher,; Horváth, John,; Jaffard, Stéphane,; Jawerth, Björn,; Johnstone, Iain M.,; Kovačević, Jelena,; Kovácević, Jelena,; Lawton, Wayne M.,; Lemarié, P. G.,; Madych, W. R.,; Mallat, Stephane G.,; Meyer, Y.,; Meyer, Yves,; Mintzer, Fred,; Morlet, J.,; Paul, T.,; Popov, Vasil,; Rokhlin, V.,; Ryan, Robert D.,; Shapiro, Jerome M.,; Smith, M.J.T.,; Strömberg, Jan-Olov,; VETIERLI, Martin,; Vaidyanathan, P,; Vetterli, Martin,; Walnut, David,; Webber, S. A.,; Weiss, Guido,; Werth, Björn Ja,; Wickerhauser, Mladen Victor,; Zimmermann, Georg,
• TeilnehmendeR: Daubechies, Ingrid.
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2009]; ©2006
• Year of Publication: 2009
• Edition: Course Book
• Language: English
• Physical Description: 1 online resource (912 p.)

This book traces the prehistory and initial development of wavelet theory, a discipline that has had a profound impact on mathematics, physics, and engineering. Interchanges between these fields during the last fifteen years have led to a number of advances in applications such as image compression,...

Table of Contents

• 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