This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris. - Provides a broad perspective on the principles and applications of transient signal processing with wavelets - Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms - Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements - Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet - Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition - Optical flow calculation and video compression algorithms - Image models with bounded variation functions - Bayes and Minimax theories for signal estimation - 200 pages rewritten and most illustrations redrawn - More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Professor Noubari's recommendation: "Professor Starks book provides an effective entry into the field for engineering students who have little or no prior knowledge of this important subject. Avaibility of collection of computer codes and mfiles in combination with topics of the book, makes the book highly valuable to enhance student learning of the subject matter."

This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets. With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. The text is written in a clear, accessible style avoiding unnecessary abstractions and details. From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification. Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the World Wide Web. Topics and Features Continuous wavelet and Gabor transforms Frame-based theory of discretization and reconstruction of analog signals is developed New and efficient "overcomplete" wavelet transform is introduced and applied Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems. Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools. The present, softcover reprint is designed to make this classic textbook available to a wider audience. A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy topic...is a class of ‘overcomplete wavelets’. These functions are not orthonormal and they lead to many useful results. —Journal of Mathematical Psychology

Introduced nearly three decades ago as a variable resolution alternative to the Fourier transform, a wavelet is a short oscillatory waveform for analysis of transients. The discrete wavelet transform has remarkable multi-resolution and energy-compaction properties. Amir-Homayoon Najmi’s introduction to wavelet theory explains this mathematical concept clearly and succinctly. Wavelets are used in processing digital signals and imagery from myriad sources. They form the backbone of the JPEG2000 compression standard, and the Federal Bureau of Investigation uses biorthogonal wavelets to compress and store its vast database of fingerprints. Najmi provides the mathematics that demonstrate how wavelets work, describes how to construct them, and discusses their importance as a tool to investigate and process signals and imagery. He reviews key concepts such as frames, localizing transforms, orthogonal and biorthogonal bases, and multi-resolution. His examples include the Haar, the Shannon, and the Daubechies families of orthogonal and biorthogonal wavelets. Our capacity and need for collecting and transmitting digital data is increasing at an astonishing rate. So too is the importance of wavelets to anyone working with and analyzing digital data. Najmi’s primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.

Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.

From the reviews: "[...] the interested reader will find in Bremaud’s book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." Mathematical Reviews