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The ultimate objective of brain-computer interface (BCI) is to provide humans an alternative communication channel allowing direct transmission of messages from the brain to a computer by analyzing the brain’s mental activities. The BCI is usually described that a person has the ability to communicate with others without the prerequisite of brain’s normal output pathways of peripheral nerves and muscles by controlling his own electroencephalographic (EEG) signals. In BCI applications, the performance and reliability of mental task analysis greatly depend on feature extraction and representation. In this book, a series of methods are proposed, including t-test-weighted time-scale plot, active segment selection, multiresolution fractal feature vector (MFFV) associated with genetic algorithm (GA), and neuro-fuzzy time-series prediction to effectively extract, select, and represent features for better classification accuracy. Compared to other well-known approaches, the experimental results show that the proposed methods are superior on both real finger movement and motor-imagery (MI) data for BCI applications.

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This distinctly accessible introduction to wavelets provides computer graphics professionals and researchers with the mathematical foundations for understanding and applying this powerful tool.Wavelets are rapidly becoming a core technique in computer graphics, with applications for* Image editing and compression* Automatic level-of-detail control for editing and rendering curves and surfaces* Surface reconstruction from contours* Physical simulation for global illumination and animationStressing intuition and clarity, this book offers a solid understanding of the theory of wavelets and their proven applications in computer graphics.Although previous introductions to wavelets have presented an elegant mathematical framework, that framework is too restrictive to apply to many problems in graphics. In contrast, this book focuses on a generalized theory that naturally accommodates the kinds of objects that commonly arise in computer graphics, including images, open curves, and surfaces of arbitrary topology.This book also contains a foreword by Ingrid Daubechies and an appendix covering the necessary background material in linear algebra.

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases that have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases that have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

This book explains wavelets to both engineers and mathematicians. It approaches the subject with a major emphasis on the filter structures attached to wavelets. Those filters are the key to algorithmic efficiency and they are well developed throughout signal processing. Now they make possible major achievements in data analysis and compression. The explanations of difficult topics are direct, rigorous and very approachable. Many practical applications are discussed. The book is ideal as an introduction to the principles of wavelets and as a reference for the analysis and applications. Also included in Wavelets and Filter Banks are many examples to make effective use of the MATLAB Wavelet Toolbox.

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Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases that have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

A Wavelet Tour of Signal Processing begins with a presentation of the wonders of the Fourier transform, and then describes its failures for transient signal processing. It presents local time–frequency methods and the related mathematical tools. The book uses an intuitive approach to important mathematical results, and emphasizes practical applications rather than proofs. It describes numerical discrete algorithms as well as some applications to information processing, fractal analysis, noise removal, and compact signal coding.A Wavelet Tour of Signal Processing is intended for signal processing engineers who want to discover the potential applications of recent mathematical advances in time–frequency signal representations. Of interest to researchers in applied mathematics, the book highlights the applications of these new techniques and also provides an overview of signal processing problems. Emphasizes practical applications rather than proofsPresents local time–frequency methods and the related mathematical toolsUses an intuitive approach to important mathematical results

Over the last two years, wavelet methods have shown themselves to be of considerable use to harmonic analysts and, in particular, advances have been made concerning their applications. The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing. Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase.

With applications in pattern recognition, data compression and numerical analysis, the wavelet transform is a key area of modern mathematics that brings new approaches to the analysis and synthesis of signals. This book presents the central issues and emphasizes comparison, assessment and how to combine method and application. It reviews different approaches to guide researchers to appropriate classes of techniques.

The ultimate objective of brain-computer interface (BCI) is to provide humans an alternative communication channel allowing direct transmission of messages from the brain to a computer by analyzing the brain’s mental activities. The BCI is usually described that a person has the ability to communicate with others without the prerequisite of brain’s normal output pathways of peripheral nerves and muscles by controlling his own electroencephalographic (EEG) signals. In BCI applications, the performance and reliability of mental task analysis greatly depend on feature extraction and representation. In this book, a series of methods are proposed, including t-test-weighted time-scale plot, active segment selection, multiresolution fractal feature vector (MFFV) associated with genetic algorithm (GA), and neuro-fuzzy time-series prediction to effectively extract, select, and represent features for better classification accuracy. Compared to other well-known approaches, the experimental results show that the proposed methods are superior on both real finger movement and motor-imagery (MI) data for BCI applications.

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases that have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

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 waveletsEmphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithmsNumerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurementsAlgorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the InternetContent 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 algorithmsImage models with bounded variation functionsBayes and Minimax theories for signal estimation200 pages rewritten and most illustrations redrawnMore problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

From the back cover: " Time-frequency methods and phase space are well known to most physicists, engineers and mathematicians as is the traditional Fourier analysis. Recently the latter found for quite a few applications a competitor in the concept of wavelets. Crudely speaking a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position parameter. Wavelets reports on a meeting that brought together people exploring and applying these concepts in an interdisciplinary framework. The topics discussed range from purely mathematical aspects over signal analysis, seismic and acoustic applications via animal sonar systems to wavelets in compute vision. "

This book presents connections between the different aspects of wavelet and subband theory.

A central goal of signal processing is to describe real life signals, be it for computation, compression, or understanding. This book presents a unified view of wavelets and subband coding with a signal processing perspective. Covers the discrete-time case, or filter banks; development of wavelets; continuous wavelet and local Fourier transforms; efficient algorithms for filter banks and wavelet computations; and signal compression. For electrical engineers and computer scientists.

In this text, the author presents mathematical background and major wavelet applications, ranging from the digital telephone to galactic structure and creation of the universe. It discusses in detail the historic origins, the algorithms and the applications of wavelets.

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 techniquesConcentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time seriesProvides easy access to a wide spectrum of parametric and non-parametric filtering methods