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Despite its short history, wavelet theory has found applications in a remarkable diversity of disciplines: mathematics, physics, numerical analysis, signal processing, probability theory and statistics. The abundance of intriguing and useful features enjoyed by wavelet and wavelet packed transforms has led to their application to a wide range of statistical and signal processing problems. On November 16-18, 1994, a conference on Wavelets and Statistics was held at Villard de Lans, France, organized by the Institute IMAG-LMC, Grenoble, France. The meeting was the 15th in the series of the Rencontres Pranco-Belges des 8tatisticiens and was attended by 74 mathematicians from 12 different countries. Following tradition, both theoretical statistical results and practical contributions of this active field of statistical research were presented. The editors and the local organizers hope that this volume reflects the broad spectrum of the conference. as it includes 21 articles contributed by specialists in various areas in this field. The material compiled is fairly wide in scope and ranges from the development of new tools for non parametric curve estimation to applied problems, such as detection of transients in signal processing and image segmentation. The articles are arranged in alphabetical order by author rather than subject matter. However, to help the reader, a subjective classification of the articles is provided at the end of the book. Several articles of this volume are directly or indirectly concerned with several as pects of wavelet-based function estimation and signal denoising.
The last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction. Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering. As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression.
The definite mathematical treatment of this important area, written by one of the founders of the field.
This is a reissue of Professor Batchelor's text on the theory of turbulent motion, which was first published by Cambridge Unviersity Press in 1953. It continues to be widely referred to in the professional literature of fluid mechanics, but has not been available for several years. This classic account includes an introduction to the study of homogeneous turbulence, including its mathematic representation and kinematics. Linear problems, such as the randomly-perturbed harmonic oscillator and turbulent flow through a wire gauze, are then treated. The author also presents the general dynamics of decay, universal equilibrium theory, and the decay of energy-containing eddies. There is a renewed interest in turbulent motion, which finds applications in atmospheric physics, fluid mechanics, astrophysics, and planetary science.
LE TRAVAIL EFFECTUE DANS CETTE THESE CONSISTE EN LA DEFINITION ET L'IMPLEMENTATION D'ALGORITHMES RAPIDES A BASE D'ONDELETTES POUR APPROCHER L'INVERSE D'OPERATEURS ELLIPTIQUES A COEFFICIENTS VARIABLES, ASSOCIES A UNE FORME SESQUILINEAIRE, CONTINUE ET COERCIVE, DE TYPE I - DIV(A*) OU A EST LIPSCHITZIENNE. LE SCHEMA UTILISE POUR CALCULER L'INVERSE EXPLICITE DE CE TYPE D'OPERATEURS REPOSE SUR D'IMPORTANTES PROPRIETES DE LOCALISATION ET D'OSCILLATION DES ONDELETTES. CES DERNIERES PERMETTENT D'UTILISER UNE NOTION DE PARAPRODUIT, QUI CONSISTE A APPROCHER LOCALEMENT L'OPERATEUR A COEFFICIENTS VARIABLES PAR UN AUTRE A COEFFICIENTS CONSTANTS. CECI DONNE ALORS NAISSANCE A UNE SORTE DE PARAMETRIX, QUI JOUE LE ROLE DE PRECONDITIONNEUR. LA CONVERGENCE DE CE SCHEMA EST ASSUREE PAR LA CONTINUITE DE CETTE PARAMETRIX ET PAR LE FAIT QUE L'ACTION DE CETTE PARAMETRIX SUR LES ONDELETTES PRODUIT DES FONCTIONS SEMBLABLES AUX ONDELETTES, APPELEES VAGUELETTES. CE SCHEMA EST DIVISE EN DEUX ETAPES. LA PREMIERE PRODUIT UNE ESTIMATION DE L'INVERSE DE L'OPERATEUR A PARTIR D'UNE APPROXIMATION GROSSIERE DONNEE PAR UNE METHODE DE GALERKIN, SUPERPOSEE A UNE APPROXIMATION DE DETAILS, OBTENUE DANS UNE BASE D'ONDELETTES D'ECHELLES SUFFISAMMENT PETITES, GRACE A LA PARAMETRIX. LA DEUXIEME ETAPE EST UN RAFFINEMENT ITERATIF DE CETTE APPROXIMATION, REALISE PAR UNE METHODE CLASSIQUE DE CORRECTION DE RESIDU. NOUS PRESENTONS DES RESULTATS NUMERIQUES EN DIMENSION 1 ET 2 POUR DIFFERENTS TYPES DE A AINSI QU'UNE ETUDE DETAILLEE DE LA COMPLEXITE ET DE LA PRECISION