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Wavelets From A Statistical Perspective
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Book Synopsis Wavelets from a Statistical Perspective by : Maarten Jansen
Download or read book Wavelets from a Statistical Perspective written by Maarten Jansen and published by CRC Press. This book was released on 2022-04-18 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data. One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material.
Book Synopsis Wavelets from a Statistical Perspective by : Maarten Jansen
Download or read book Wavelets from a Statistical Perspective written by Maarten Jansen and published by CRC Press. This book was released on 2022-04-18 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data. One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material.
Book Synopsis Essential Wavelets for Statistical Applications and Data Analysis by : Todd Ogden
Download or read book Essential Wavelets for Statistical Applications and Data Analysis written by Todd Ogden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Wavelet Methods in Statistics with R by : Guy Nason
Download or read book Wavelet Methods in Statistics with R written by Guy Nason and published by Springer Science & Business Media. This book was released on 2010-07-25 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Wavelets, Approximation, and Statistical Applications by : Wolfgang Härdle
Download or read book Wavelets, Approximation, and Statistical Applications written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Wavelets and Statistics by : Anestis Antoniadis
Download or read book Wavelets and Statistics written by Anestis Antoniadis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Wavelet Methods for Time Series Analysis by : Donald B. Percival
Download or read book Wavelet Methods for Time Series Analysis written by Donald B. Percival and published by Cambridge University Press. This book was released on 2006-02-27 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to wavelet analysis 'from the ground level and up', and to wavelet-based statistical analysis of time series focuses on practical discrete time techniques, with detailed descriptions of the theory and algorithms needed to understand and implement the discrete wavelet transforms. Numerous examples illustrate the techniques on actual time series. The many embedded exercises - with complete solutions provided in the Appendix - allow readers to use the book for self-guided study. Additional exercises can be used in a classroom setting. A Web site offers access to the time series and wavelets used in the book, as well as information on accessing software in S-Plus and other languages. Students and researchers wishing to use wavelet methods to analyze time series will find this book essential.
Book Synopsis Wavelets, Approximation and Statistical Applications by : Wolfgang Härdle
Download or read book Wavelets, Approximation and Statistical Applications written by Wolfgang Härdle and published by John Wiley & Sons. This book was released on 1997-09-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to various aspects of wavelets. Along with presenting theory, this book discusses approximations and gives a variety of statistical applications. It includes software codes for all applications discussed.Contains information on the theory and construction of wavelets previously only available in journals. -- Brings together the three main areas of wavelet theory.
Book Synopsis Wavelet Packets and Their Statistical Applications by : Khalil Ahmad
Download or read book Wavelet Packets and Their Statistical Applications written by Khalil Ahmad and published by Springer. This book was released on 2018-06-21 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Antieigenvalue Analysis by : Karl Gustafson
Download or read book Antieigenvalue Analysis written by Karl Gustafson and published by World Scientific. This book was released on 2012 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.
Book Synopsis Applied Wavelet Analysis with S-PLUS by : Andrew Bruce
Download or read book Applied Wavelet Analysis with S-PLUS written by Andrew Bruce and published by Springer Science & Business Media. This book was released on 1996-06-20 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a visual data analysis approach, wavelet concepts are explained in a way that is intuitive and easy to understand. Furthermore, in addition to wavelets, a whole range of related signal processing techniques such as wavelet packets, local cosine analysis, and matching pursuits are covered, and applications of wavelet analysis are illustrated -including nonparametric function estimation, digital image compression, and time-frequency signal analysis. This book and software package is intended for a broad range of data analysts, scientists, and engineers. While most textbooks on the subject presuppose advanced training in mathematics, this book merely requires that readers be familiar with calculus and linear algebra at the undergraduate level.
Book Synopsis Wavelet Methods in Statistics with R by : G. P. Nason
Download or read book Wavelet Methods in Statistics with R written by G. P. Nason and published by Springer Science & Business Media. This book was released on 2008-08-11 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Wavelets, Approximation, and Statistical Applications by : Wolfgang Härdle
Download or read book Wavelets, Approximation, and Statistical Applications written by Wolfgang Härdle and published by . This book was released on 1998 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Wavelets and Statistics by : Anestis Antoniadis
Download or read book Wavelets and Statistics written by Anestis Antoniadis and published by . This book was released on 1995-07-27 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wavelets written by Desanka P. Radunovic and published by Springer. This book was released on 2010-10-22 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real world phenomena are permanently changing with various speeds of change. Repeating of four seasons in a year accompanied by appropriate changes in nature, alternation of day and night within twenty four hours, heart pulsations, air vibra tions that produce sound or stock-market fluctuations are only several examples. Furthermore, since most of these problems express nonlinear effects characterized by fast and short changes, small waves or wavelets are an ideal modeling tool. An oscillatory property and multiresolution nature of wavelets recommends them for use both in signal processing and in solving complex mathematical models of real world phenomena. As a professor at the School of Mathematics, who teaches computer science students, I feel the need to bridge' the gap between the theoretical and practical aspects of wavelets. On the one side, mathematicians need help to implement wavelet theory in solving practical problems. On the other side, engineers and other practitioners need help in understanding how wavelets work in order to be able to create new or modify the existing wavelets according to their needs. This book tries to satisfy both wavelet user groups; to present and explain the mathematical bases of the wavelet theory and to link them with some of the a~eas where this theory is already being successfully applied. It is self contained and no previous knowledge is assumed. The introductory chapter gives a short overview of the development of the wavelet concept from its origins at the beginning ofthe twentieth century until now.
Book Synopsis Fundamentals of Wavelets by : Jaideva C. Goswami
Download or read book Fundamentals of Wavelets written by Jaideva C. Goswami and published by John Wiley & Sons. This book was released on 2011-03-08 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most existing books on wavelets are either too mathematical or they focus on too narrow a specialty. This book provides a thorough treatment of the subject from an engineering point of view. It is a one-stop source of theory, algorithms, applications, and computer codes related to wavelets. This second edition has been updated by the addition of: a section on "Other Wavelets" that describes curvelets, ridgelets, lifting wavelets, etc a section on lifting algorithms Sections on Edge Detection and Geophysical Applications Section on Multiresolution Time Domain Method (MRTD) and on Inverse problems
Book Synopsis Wavelet Analysis on Local Fields of Positive Characteristic by : Biswaranjan Behera
Download or read book Wavelet Analysis on Local Fields of Positive Characteristic written by Biswaranjan Behera and published by Springer Nature. This book was released on 2022-01-01 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.
