Fundamentals of Wavelets

Provides a solid yet accessible mathematical foundation for those interested in learning about wavelets & pursuing the broad range of applications for which the wavelet transform has proved successful. ...

"Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago by Morlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering. Classical wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach....

How (and why) this book is different
Wavelets are incredibly powerful, but if you can t understand them, you can t use them or worse, blissfully misuse them!
CONCEPTUAL WAVELETS is unique as a complete, in-depth treatment of the subject but from an intuitive, conceptual point of view. In this book we stress informed use of wavelets and leave the mathematically rigorous proofs to other texts. We do look at some key equations (at a high-school algebra level)--but only after the concepts are demonstrated so you can see the wavelets (and their associated equations) in action.

The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques....

7111119142Written by a successful author and respected mathematician, this book emphasizes a concrete and computational approach to the subject of Fourier analysis and wavelet theory while maintaining a balance between theory and applications. In some cases, several different proofs are offered for a given proposition, allowing students to compare different methods. ...

Since their appearance in mid-1980s, wavelets and, more generally, multiscale methods have become powerful tools in mathematical analysis and in applications to numerical analysis and signal processing. This book is based on "Ondelettes et Traitement Numerique du Signal" by Albert Cohen. It has been translated from French by Robert D. Ryan and extensively updated by both Cohen and Ryan. It studies the existing relations between filter banks and wavelet decompositions and shows how these relations can be exploited in the context of digital signal processing. ...

This comprehensive monograph presents the history and achievements of one of the most important figures in modern mathematics, covering the work of Fourier from his first memoir on the Analytical Theory of Heat to the latest developments in wavelet theory. Originally, Fourier series were used to describe and compute the functions which occur in heat diffusion and equilibrium, but they soon led to the development of new theories by Fourier's followers, and some of these original papers are considered in this text. ...

This book in its third edition additionally explores how the ubiquitous electronic spreadsheet can be utilized for wavelet based signal and image processing. Many of the intriguing properties of wavelet and scaling functions can be easily observed in the spreadsheets.

[list][*]Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing)[*]Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques...

0387578846The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis. It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics. ...

Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling ? self-similarity, long-range dependence and multi-fractals ? are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space. ...

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