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, turbulence, machine vision, radar, and earthquake prediction. This book contains the seminal papers that presented the ideas from which wavelet theory evolved, as well as those major papers that developed the theory into its current form. These papers originated in a variety of journals from different disciplines, making it difficult for the researcher to obtain a complete view of wavelet theory and its origins. Additionally, some of the most significant papers have heretofore been available only in French or German. Heil and Walnut bring together these documents in a book that allows researchers a complete view of wavelet theory's origins and development.

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