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Author: Maarten Jansen
Publisher: CRC Press
ISBN: 1000564142
Category : Business & Economics
Languages : en
Pages : 346
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Book Description
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.
Author: Maarten Jansen
Publisher: CRC Press
ISBN: 1000564142
Category : Business & Economics
Languages : en
Pages : 346
Get Book Here
Book Description
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.
Author: Donald B. Percival
Publisher: Cambridge University Press
ISBN: 1107717396
Category : Mathematics
Languages : en
Pages : 628
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Book Description
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.
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: Houman Owhadi
Publisher: Cambridge University Press
ISBN: 1108484360
Category : Mathematics
Languages : en
Pages : 491
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Book Description
Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.
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: Ramazan Gençay
Publisher: Elsevier
ISBN: 0080509223
Category : Business & Economics
Languages : en
Pages : 383
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Book Description
An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method. - The first book to present a unified view of filtering techniques - Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series - Provides easy access to a wide spectrum of parametric and non-parametric filtering methods
Author: G. P. Nason
Publisher: Springer Science & Business Media
ISBN: 9780387759609
Category : Business & Economics
Languages : en
Pages : 276
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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: Maarten Jansen
Publisher:
ISBN: 9781032208206
Category : Statistics
Languages : en
Pages : 0
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Book Description
Cover -- Half Title -- Title Page -- Copyright Page -- Table of contents -- List of recurrent symbols -- Introduction -- The topic of this book -- For whom has this book been written? -- The exercises -- Accompanying software -- Acknowledgements -- 1. Wavelets: nonlinear processing in multiscale sparsity -- 1.1. Compressing big data -- 1.2. Wavelets among other methods for data processing -- 1.2.1. The Fourier transform -- 1.2.2. Using Fourier analysis in linear data processing -- 1.2.3. From sines to splines -- 1.2.4. Regression splines, smoothing splines, P-splines -- 1.2.5. Kernels and local polynomial smoothing -- 1.3. An illustrative example of a wavelet decomposition -- 1.3.1. A test function with jumps and cusps -- 1.3.2. Linear smoothing -- 1.3.3. A Fourier analysis of data with discontinuities -- 1.3.4. A multilevel approach -- 1.3.5. The Haar transform -- 1.3.6. The Haar basis -- 1.3.7. Wavelet basis functions -- 1.3.8. The Haar transform matrix -- 1.4. The key properties of a wavelet method -- 1.5. Intrinsic multiscale problems -- 1.6. Design of a wavelet transform -- 1.6.1. Perfect reconstruction (PR) -- 1.6.2. Fast decomposition and reconstruction -- 1.6.3. The characteristics of the basis functions -- 1.6.4. The sparsity of the decomposition -- 1.6.5. Numerical condition -- 1.7. Conclusion -- 2. Wavelet building blocks -- 2.1. From the Haar transform to the lifting scheme -- 2.1.1. Nonequidistant grids -- 2.1.2. The unbalanced Haar transform -- 2.1.3. The Haar transform as a lifting scheme -- 2.1.4. A prediction-first scheme for the same unbalanced Haar transform -- 2.1.5. Triangular hat basis functions -- 2.1.6. Wavelets in a triangular hat basis -- 2.1.7. A general two-step lifting scheme -- 2.1.7.1. Prediction-first scheme -- 2.1.7.2. Update-first (in the forward transform) -- 2.1.8. Lifting in diagrams -- 2.2. Filterbanks.
Author: Stephane Mallat
Publisher: Elsevier
ISBN: 0080520839
Category : Computers
Languages : en
Pages : 663
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Book Description
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
Author: Charles K. Chui
Publisher: Elsevier
ISBN: 1483282864
Category : Science
Languages : en
Pages : 281
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Book Description
Wavelet Analysis and its Applications, Volume 1: An Introduction to Wavelets provides an introductory treatise on wavelet analysis with an emphasis on spline-wavelets and time-frequency analysis. This book is divided into seven chapters. Chapter 1 presents a brief overview of the subject, including classification of wavelets, integral wavelet transform for time-frequency analysis, multi-resolution analysis highlighting the important properties of splines, and wavelet algorithms for decomposition and reconstruction of functions. The preliminary material on Fourier analysis and signal theory is covered in Chapters 2 and 3. Chapter 4 covers the introductory study of cardinal splines, while Chapter 5 describes a general approach to the analysis and construction of scaling functions and wavelets. Spline-wavelets are deliberated in Chapter 6. The last chapter is devoted to an investigation of orthogonal wavelets and wavelet packets. This volume serves as a textbook for an introductory one-semester course on "wavelet analysis for upper-division undergraduate or beginning graduate mathematics and engineering students.
