Wavelet Theory And Harmonic Analysis In Applied Sciences

Author : Carlos E. D'Attellis,Elena M. Fernandez-Berdaguer
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461220107

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Wavelet Theory and Harmonic Analysis in Applied Sciences by Carlos E. D'Attellis,Elena M. Fernandez-Berdaguer Pdf

The idea of this book originated in the works presented at the First Latinamerican Conference on Mathematics in Industry and Medicine, held in Buenos Aires, Argentina, from November 27 to December 1, 1995. A variety of topics were discussed at this meeting. A large percentage of the papers focused on Wavelet and Harmonic Analysis. The theory and applications of this topic shown at the Conference were interesting enough to be published. Based on that we selected some works which make the core of this book. Other papers are contributions written by invited experts in the field to complete the presentation. All the works were written after the Conference. The purpose of this book is to present recent results as well as theo retical applied aspects of the subject. We have decided not to include a section devoted to the theoretical foundations of wavelet methods for non specialists. There are excellent introductions already available, for example, Chapter one in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser, 1996, or some of the references cited in the chapter.

Author : Carlos E D'Attellis,Elena M Fernandez-Berdaguer
Publisher : Unknown
Page : 368 pages
File Size : 49,6 Mb
Release : 1997-07-01
Category : Electronic
ISBN : 1461220114

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Wavelet Theory and Harmonic Analysis in Applied Sciences by Carlos E D'Attellis,Elena M Fernandez-Berdaguer Pdf

Author : Peter Roberts
Publisher : New Age International
Page : 180 pages
File Size : 50,7 Mb
Release : 2007
Category : Wavelets (Mathematics)
ISBN : 8122415156

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Wavelet Analysis And Applications by Peter Roberts Pdf

Wavelets And Related Functions Constitute A Most Recent Set Of Mathematical Tools, Impacting Many Branches Of Mathematical And Applied Sciences, Ranging From Approximation Theory And Harmonic Analysis To Signal Analysis And Image Compression.This Volume Includes Lectures Delivered At The Platinum Jubilee Workshop And Tenth Ramanujan Symposium, Pjwtrs-2003, On Wavelet Analysis, Conducted In March 2003. The Contents Cover A Variety Of Interesting Topics Like Wavelets As Approximation Tools, Connections With Filter Banks, The Bessel-Wavelet Transform, Relations With Partial Differential Equations Of Fluid Flow, Weyl Heisenberg Frames, Reconstruction Of Functions From Irregular Sampling And Various Applications, Particularly In Electrical Engineering. This Book Will Be Useful To Mathematicians, Computer And Electrical Engineers, Systems Analysts And Applied Scientists. The Level Can Be Graduate Engineer Or Post Graduate Student Of Mathematics.

Author : Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate
Publisher : Birkhäuser
Page : 256 pages
File Size : 43,7 Mb
Release : 2015-09-12
Category : Mathematics
ISBN : 9783319188638

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Harmonic and Applied Analysis by Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate Pdf

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.​

Author : Ola Bratteli,Palle Jorgensen
Publisher : Birkhäuser
Page : 398 pages
File Size : 40,7 Mb
Release : 2013-11-29
Category : Mathematics
ISBN : 1461264154

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Wavelets Through a Looking Glass by Ola Bratteli,Palle Jorgensen Pdf

? Concise background material for each chapter, open problems, exercises, bibliography, and comprehensive index make this work a fine pedagogical and reference resource.; New previously unpublished results appear on the homotopy of multiresolutions, approximation theory, the spectrum and structure of the fixed points of the associated transfer, subdivision operators; Key topics of wavelet theory are examined; Excellent graphics show how wavelets depend on the spectra of the transfer operators; The important role of the spectrum of a transfer operator is studied; This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory.

Author : Anthony Teolis
Publisher : Birkhäuser
Page : 324 pages
File Size : 55,7 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9783319657479

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Computational Signal Processing with Wavelets by Anthony Teolis Pdf

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

Author : Don Hong,Jianzhong Wang,Robert Gardner
Publisher : Elsevier
Page : 387 pages
File Size : 47,8 Mb
Release : 2004-12-31
Category : Mathematics
ISBN : 9780080540313

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Real Analysis with an Introduction to Wavelets and Applications by Don Hong,Jianzhong Wang,Robert Gardner Pdf

Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications. The text is relatively elementary at the start, but the level of difficulty steadily increases The book contains many clear, detailed examples, case studies and exercises Many real world applications relating to measure theory and pure analysis Introduction to wavelet analysis

Author : David F. Walnut
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 54,7 Mb
Release : 2013-12-11
Category : Computers
ISBN : 9781461200017

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An Introduction to Wavelet Analysis by David F. Walnut Pdf

This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.

Author : John J. Benedetto
Publisher : CRC Press
Page : 592 pages
File Size : 46,5 Mb
Release : 2021-07-28
Category : Mathematics
ISBN : 9781000443462

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Wavelets by John J. Benedetto Pdf

Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461201373

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Wavelet Transforms and Time-Frequency Signal Analysis by Lokenath Debnath Pdf

The last fifteen years have produced major advances in the mathematical theory of wavelet transforms and their applications to science and engineering. In an effort to inform researchers in mathematics, physics, statistics, computer science, and engineering and to stimulate furtherresearch, an NSF-CBMS Research Conference on Wavelet Analysis was organized at the University of Central Florida in May 1998. Many distinguished mathematicians and scientists from allover the world participated in the conference and provided a digest of recent developments, open questions, and unsolved problems in this rapidly growing and important field. As a follow-up project, this monograph was developed from manuscripts sub mitted by renowned mathematicians and scientists who have made important contributions to the subject of wavelets, wavelet transforms, and time-frequency signal analysis. This publication brings together current developments in the theory and applications of wavelet transforms and in the field of time-frequency signal analysis that are likely to determine fruitful directions for future advanced study and research.

Author : Tao Qian,Mang I. Vai,Yuesheng Xu
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 53,7 Mb
Release : 2007-02-24
Category : Mathematics
ISBN : 9783764377786

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Wavelet Analysis and Applications by Tao Qian,Mang I. Vai,Yuesheng Xu Pdf

This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.

Author : Jonathan Cohen,Ahmed I. Zayed
Publisher : Birkhäuser
Page : 338 pages
File Size : 53,6 Mb
Release : 2011-03-09
Category : Mathematics
ISBN : 0817680942

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Wavelets and Multiscale Analysis by Jonathan Cohen,Ahmed I. Zayed Pdf

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, 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. Overall, the book is an excellent reference for graduate students, researchers, and practitioners in theoretical and applied mathematics, or in engineering.

Author : Carlo Cattani
Publisher : World Scientific
Page : 473 pages
File Size : 41,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812709769

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Wavelet and Wave Analysis as Applied to Materials with Micro Or Nanostructure by Carlo Cattani Pdf

This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three. All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problems that are proposed in this book. By combining these new scientific concepts into a unitary model and enlightening readers on this pioneering field of research, readers will hopefully be inspired to explore the more advanced aspects of this promising scientific direction. The application of wavelet analysis to nanomaterials and waves in nanocomposites can be very appealing to both specialists working on theoretical developments in wavelets as well as specialists applying these methods and experiments in the mechanics of materials. Sample Chapter(s). Chapter 1: Introduction (121 KB). Contents: Wavelet Analysis; Materials with Micro- or Nanostructure; Waves in Materials; Simple and Solitary Waves in Materials; Solitary Waves and Elastic Waves. Readership: Advanced undergraduate and graduate students as well as experts in mathematical modeling, engineering mechanics and mechanics, physics; specialists in wavelet and wave analysis as tools for mathematical modeling.

Author : Brigitte Forster,Peter Robert Massopust
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 46,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780817648909

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Four Short Courses on Harmonic Analysis by Brigitte Forster,Peter Robert Massopust Pdf

Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory, wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory.

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200253

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Wavelets and Signal Processing by Lokenath Debnath Pdf

Provides a digest of the current developments, open questions and unsolved problems likely to determine a new frontier for future advanced study and research in the rapidly growing areas of wavelets, wavelet transforms, signal analysis, and signal and image processing. Ideal reference work for advanced students and practitioners in wavelets, and wavelet transforms, signal processing and time-frequency signal analysis. Professionals working in electrical and computer engineering, applied mathematics, computer science, biomedical engineering, physics, optics, and fluid mechanics will also find the book a valuable resource.