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Author: Khalil Ahmad
Publisher: Springer
ISBN: 9811302685
Category : Mathematics
Languages : en
Pages : 249
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Book Description
This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising.
Author: Khalil Ahmad
Publisher: Springer
ISBN: 9811302685
Category : Mathematics
Languages : en
Pages : 249
Get Book Here
Book Description
This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising.
Author: Todd Ogden
Publisher: Springer Science & Business Media
ISBN: 1461207096
Category : Technology & Engineering
Languages : en
Pages : 218
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Book Description
I once heard the book by Meyer (1993) described as a "vulgarization" of wavelets. While this is true in one sense of the word, that of making a sub ject popular (Meyer's book is one of the early works written with the non specialist in mind), the implication seems to be that such an attempt some how cheapens or coarsens the subject. I have to disagree that popularity goes hand-in-hand with debasement. is certainly a beautiful theory underlying wavelet analysis, there is While there plenty of beauty left over for the applications of wavelet methods. This book is also written for the non-specialist, and therefore its main thrust is toward wavelet applications. Enough theory is given to help the reader gain a basic understanding of how wavelets work in practice, but much of the theory can be presented using only a basic level of mathematics. Only one theorem is for mally stated in this book, with only one proof. And these are only included to introduce some key concepts in a natural way.
Author: Guy Nason
Publisher: Springer Science & Business Media
ISBN: 0387759611
Category : Mathematics
Languages : en
Pages : 259
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Book Description
This book contains information on how to tackle many important problems using a multiscale statistical approach. It focuses on how to use multiscale methods and discusses methodological and applied considerations.
Author: Anestis Antoniadis
Publisher: Springer Science & Business Media
ISBN: 1461225442
Category : Mathematics
Languages : en
Pages : 407
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Book Description
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.
Author: Wolfgang Härdle
Publisher: Springer Science & Business Media
ISBN: 1461222222
Category : Mathematics
Languages : en
Pages : 276
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Book Description
The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap proximation of possibly irregular functions and surfaces and was successfully applied in data compression, turbulence analysis, image and signal process ing. Five years ago wavelet theory progressively appeared to be a power ful framework for nonparametric statistical problems. Efficient computa tional implementations are beginning to surface in this second lustrum of the nineties. This book brings together these three main streams of wavelet theory. It presents the theory, discusses approximations and gives a variety of statistical applications. It is the aim of this text to introduce the novice in this field into the various aspects of wavelets. Wavelets require a highly interactive computing interface. We present therefore all applications with software code from an interactive statistical computing environment. Readers interested in theory and construction of wavelets will find here in a condensed form results that are somewhat scattered around in the research literature. A practioner will be able to use wavelets via the available software code. We hope therefore to address both theory and practice with this book and thus help to construct bridges between the different groups of scientists. This te. xt grew out of a French-German cooperation (Seminaire Paris Berlin, Seminar Berlin-Paris). This seminar brings together theoretical and applied statisticians from Berlin and Paris. This work originates in the first of these seminars organized in Garchy, Burgundy in 1994.
Author: Michel Misiti
Publisher: John Wiley & Sons
ISBN: 1118613597
Category : Technology & Engineering
Languages : en
Pages : 270
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Book Description
The last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction. Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering. As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression.
Author: Deukwoo Kwon
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Wavelet methods possess versatile properties for statistical applications. We would like to explore the advantages of using wavelets in the analyses in two different research areas. First of all, we develop an integrated tool for online detection of network anomalies. We consider statistical change point detection algorithms, for both local changes in the variance and for jumps detection, and propose modified versions of these algorithms based on moving window techniques. We investigate performances on simulated data and on network traffic data with several superimposed attacks. All detection methods are based on wavelet packets transformations. We also propose a Bayesian model for the analysis of high-throughput data where the outcome of interest has a natural ordering. The method provides a unified approach for identifying relevant markers and predicting class memberships. This is accomplished by building a stochastic search variable selection method into an ordinal model. We apply the methodology to the analysis of proteomic studies in prostate cancer. We explore wavelet-based techniques to remove noise from the protein mass spectra. The goal is to identify protein markers associated with prostate-specific antigen (PSA) level, an ordinal diagnostic measure currently used to stratify patients into different risk groups.
Author: J.S. Byrnes
Publisher: Springer Science & Business Media
ISBN: 9780792330783
Category : Mathematics
Languages : en
Pages : 432
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Book Description
It is probably true quite generally that in the history of human thinking the most fruitful developments frequently take place at those points where two different lines of thought meet. Hence, if they actually meet, that is, if they are at least so much related to each other that a real interaction can take place, then one may hope that new and interesting developments may follow. Werner Heisenberg This volume contains papers presented at the August 1992 NATO Advanced Study Institute on Wavelets and Their Applications. The conference was held at the beautiful Il Ciocco resort near Lucca, in the glorious Tuscany region of northern Italy. Once again we gathered at this idyllic spot to explore and extend the reciprocity between mathematics and engineering. The dynamic interaction between world-renowned scientists from the usu ally disparate communities of pure mathematicians and applied scientists, which occurred at our 1989 and 1991 ASI's, continued at this meeting. Wavelet theory and technology is in an important growth stage at which theoretical and practical results are being compared with existing methods. There have been spectacular wavelet successes and sobering comparisons with traditional ideas-but still there is a wide expanse of scientific problems to explore. Since these problems lie at the forefront of both pure mathematics and applied science, our NATO ASI was especially pertinent at this time.
Author: Patrick J. Van Fleet
Publisher: John Wiley & Sons
ISBN: 1118979273
Category : Mathematics
Languages : en
Pages : 637
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Book Description
Updated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals The new edition of Discrete Wavelet Transformations continues to guide readers through the abstract concepts of wavelet theory by using Dr. Van Fleet’s highly practical, application-based approach, which reflects how mathematicians construct solutions to challenges outside the classroom. By introducing the Haar, orthogonal, and biorthogonal filters without the use of Fourier series, Van Fleet allows his audience to connect concepts directly to real-world applications at an earlier point than other publications in the field. Leveraging extensive graphical displays, this self-contained volume integrates concepts from calculus and linear algebra into the constructions of wavelet transformations and their applications, including data compression, edge detection in images and denoising of signals. Conceptual understanding is reinforced with over 500 detailed exercises and 24 computer labs. The second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include: Two new chapters covering wavelet packets and the lifting method A reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques A new comprehensive chapter that explains filter derivation using Fourier techniques Over 120 examples of which 91 are “live examples,” which allow the reader to quickly reproduce these examples in Mathematica or MATLAB and deepen conceptual mastery An overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented A complete rewrite of the DiscreteWavelets package called WaveletWare for use with Mathematica and MATLAB A website, www.stthomas.edu/wavelets, featuring material containing the WaveletWare package, live examples, and computer labs in addition to companion material for teaching a course using the book Comprehensive and grounded, this book and its online components provide an excellent foundation for developing undergraduate courses as well as a valuable resource for mathematicians, signal process engineers, and other professionals seeking to understand the practical applications of discrete wavelet transformations in solving real-world challenges.
Author: Jian-Ping Li
Publisher: World Scientific
ISBN: 9789812388742
Category : Computers
Languages : en
Pages : 582
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Book Description
Wavelet analysis and its applications have been one of the fastest-growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, and air acoustics. Active media technology is concerned with the development of autonomous computational or physical entities capable of perceiving, reasoning, adapting, learning, cooperating, and delegating in a dynamic environment.This book captures the essence of the state of the art in wavelet analysis and its applications and active media technology. At the Congress, invited talks were delivered by distinguished researchers, namely Prof John Daugman of Cambridge University, UK; Prof Bruno Torresani of INRIA, France; Prof Victor Wickerhauser of Washington University, USA, Prof Ning Zhong of the Maebashi Institute of Technology, Japan; Prof John Yen of Pennsylvania State University, USA; and Prof Sankar K Pal of the Indian Statistical Institute, India.
