Synopses & Reviews
Since the introduction of wavelets in the early 1980s, the subject has undergone tremendous development both on the theoretical and applied fronts. Myriads of research and survey papers and monographs have been published on the subject covering different areas of applications, such as signal and image processing, denoising, data compression, tomography, and medical imaging.
A reflection of two decades of extensive research activities, this self-contained volume serves as a vehicle to look back at what has been accomplished and ponder what lies ahead in the field of wavelets. The work, which is a collection of invited chapters that are outgrowths of the talks from an international conference on wavelets, features both expository and survey chapters covering the history and major accomplishments in the field as well as new directions for wavelets, particularly in the area of geometric harmonic analysis.
Specific topics covered include:
* wavelet frames
* harmonic and multiscale analysis of and on data sets in high dimensions
* nonlinear approximations and multiresolution algorithms in high dimensions
* frame perturbations to operator algebras
* wavelets as a numerical tool for atmospheric data analysis
* wavelets and sparcity in fluids and plasmas
* locally scale invariant multifractality
* filterbanks for interpolation and denoising
Wavelets and Multiscale Analysis: Theory and Applicationsis an excellent reference for graduate students, researchers, and practitioners in mathematics, engineering, and physics.
Synopsis
Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, features expository and research articles covering current and emerging areas in the theory and applications of wavelets. The book is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings. Part II looks at the use of multiscale harmonic analysis for understanding the geometry of large data sets and extracting information from them. Part III focuses on applications of wavelet theory to the study of several real-world problems. Specific topics covered include: wavelets on locally compact groups and Riemannian manifolds;
Table of Contents
Preface.- Contributors.- 1 An Introduction to Wavelets and Multi-scale Analysis: Theory and Applications.- Part I The Mathematical Theory of Wavelets.- 2 The Construction of Wavelet Sets.- 3 The Measure of the Closure of a Wavelet Set May Be >2pi.- Quincunx Wavelets on T^2.- Crystallographic Haar-type Composite Dilation Wavelets.- 6 From Full Rank Subdivision Schemes to Multichannel Wavelets: A Constructive Approach.- 7 Unitary Systems and Bessel Generator Multipliers.- 8 The Zak Transform(s).- Part II The Geometry of Large Data Sets.- 9 Harmonic Analysis of Digital Databases.- 10 Some Recent Advances in Multiscale Geometric Analysis of Point Clouds.- 11 Signal Ensemble Classification Using Low-Dimensional Embeddings and Earth Mover's Distance.- Part III Applications of Wavelets.- 12 Wavelets on Manifolds and Statistical Applications to Cosmology.- 13 Wavelets, a Numerical Tool for Atmospheric Data Analysis.- 14 Denoising Speech Signals for Digital Hearing Aids: A Wavelet Based Approach.- Index.