本书源于由广州中山大学和上海中法应用数学学会共同组织的名为Wavelet Methods in Mathematical Analysis and Engineering的学术讨论会，该讨论会包括面向中国的博士和博士后的暑期班课程以及相关主题的学术会议。课程目的旨在提供给学生必要的小波分析及其主要应用的知识，并能让听者继续研究并受益。书中内容覆盖了小波基和交错分解方法的基本框架，概览了其在偏微分方程数值分析、信号和图像处理中的主要应用。本书可供应用数学、信号处理、图像处理及工程领域的教师、学生和科研工作者。

This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state of the art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective.

The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis.

Preface

Jianfeng Cai, Raymond Chan, Lixin Shen, Zuowei Shen:

 Tight Frame Based Method for High-Resolution Image Reconstruction

Albert Cohen: Greedy Algorithms for Adaptive Triangulations and Approximations

Stephane Jaffard, Patrice Abry, Stephane G. Roux, Beatrice Vedel, Herwig Wendt:

 The Contribution of Wavelets in Multifractal Analysis

Chaochun Liu and Daoqing Dai: Wavelet Methods for Image-Based Face Recognition: A Survey

Lihua Yang: Hilbert-Huang Transform: Its Background, Algorithms and Applications