Wavelets and Statistics

ISBN-13: 9780387945644 / Angielski / Miękka / 1995 / 414 str.

Antoeades; Anestis Antoniadis; Georges Oppenheim

Opis

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.

Spis treści

Thresholding of Wavelet Coefficients as Multiple Hypotheses Testing Procedure.- Wavelets, spectrum analysis and 1/f processes.- Variance Function Estimation in Regression by Wavelet Methods.- Locally Self Similar Gaussian Processes.- WaveLab and Reproducible Research.- Extrema Reconstructions and Spline Smoothing: Variations on an Algorithm of Mallat & Zhong..- Identification of Chirps with Continuous Wavelet Transform.- Nonlinear Approximation of Stochastic Processes.- Translation-Invariant De-Noising.- Estimating Wavelet Coefficients.- Nonparametric Supervised Image Segmentation by Energy Minimization using Wavelets.- On the Statistics of Best Bases Criteria.- Discretized Wavelet Density Estimators for Continuous Time Stochastic Processes.- Wavelets and Markov Random Fields in a Bayesian Framework.- Micronde : a Matlab Wavelet Toolbox for Signals and Images.- Wavelet Function Estimation using Cross-Validation.- The Stationary Wavelet Transform and some Statistical Applications.- Wavelet Thresholding: Beyond the Gaussian I.I.D. Situation.- L2(0,1) Weak Convergence of the Empirical Process for Dependent Variables.- Top-Down and Bottom-Up Tree Search Algorithms for Selecting Bases in Wavelet Packet Transforms.- WavBox 4: A Software Toolbox for Wavelet Transforms and Adaptive Wavelet Packet Decompositions.- Using Wavelets for Classifying Human in vivo Magnetic Resonance.- Adaptive Density Estimation.- Wavelets and Regression Analysis.- Reader’s Guide.