Lecture Notes On Wavelet Transforms

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Lecture Notes On Wavelet Transforms

Author : Lokenath Debnath
ISBN : 9783319594330
Genre : Mathematics
File Size : 85.70 MB
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This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India.
Category: Mathematics

Abstract Harmonic Analysis Of Continuous Wavelet Transforms

Author : Hartmut Führ
ISBN : 3540242597
Genre : Mathematics
File Size : 35.11 MB
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This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the volume can also be read as a problem-driven introduction to the Plancherel formula.
Category: Mathematics

Discrete Fourier And Wavelet Transforms An Introduction Through Linear Algebra With Applications To Signal Processing

Author : Roe W Goodman
ISBN : 9789814725798
Genre : Mathematics
File Size : 28.11 MB
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This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
Category: Mathematics

Wavelet Transforms And Time Frequency Signal Analysis

Author : Lokenath Debnath
ISBN : 0817641041
Genre : Mathematics
File Size : 44.38 MB
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The last two decades have produced tremendous developments in the mathematical theory of wavelets and their great variety of applications in science and engineering. Wavelets allow complex information, such as music, speech, images and patterns to be decomposed into an elementary form called 'building blocks' at different positions and scales. The information is reconstructed with high precision. In an effort to acquaint researchers in applied mathematics, physics, statistics, computer science, and engineering and to stimulate further research, a regional research convergence was organized at the University of Central Florida in May 1998. Many distinguished applied mathematicians and engineering scientists participated in the conference and presented a digest of recent developments, open questions and unsolved problems in this rapidly growing and important field. As a follow-up project, this book has developed from chapters written by renowned mathematicians and engineering scientists who have important contribution to the subject of wavelets, wavelet transforms, and time-frequency signal analysis. The carefully selected chapters in this new text will appeal to the reader interested in a broad perspective of wavelet analysis and time- frequency signal analysis. "Wavelet Transforms and Time-Frequency Signal Analysis" brings together recent developments in theory and applications of wavelet transforms that are likely to determine fruitful directions for future advanced study and research. The book is designed as a new source for modern topics dealing with wavelets, wavelet transforms, time-frequency signal analysis and other applications for future development of this new, important and useful subject for mathematics, science and engineering.
Category: Mathematics

Wavelets And Their Applications

Author : Michel Misiti
ISBN : 9781118613597
Genre : Technology & Engineering
File Size : 49.24 MB
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The last 15 years have seen an explosion of interest in waveletswith applications in fields such as image compression, turbulence,human vision, radar and earthquake prediction. Wavelets represent an area that combines signal in imageprocessing, mathematics, physics and electrical engineering. As such, this title is intended for the wide audience that isinterested in mastering the basic techniques in this subject area,such as decomposition and compression.
Category: Technology & Engineering

Wavelet Analysis And Multiresolution Methods

Author : Tian-Xiao He
ISBN : 0824704177
Genre : Mathematics
File Size : 65.77 MB
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This volume contains papers selected from the Wavelet Analysis and Multiresolution Methods Session of the AMS meeting held at the University of Illinois at Urbana-Champaign. The contributions cover: construction, analysis, computation and application of multiwavelets; scaling vectors; nonhomogenous refinement; mulivariate orthogonal and biorthogonal wavelets; and other related topics.
Category: Mathematics

Spline Functions And The Theory Of Wavelets

Author : Serge Dubuc
ISBN : 0821870181
Genre : Mathematics
File Size : 82.87 MB
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This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics. Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattered-data interpolation, differential equations and various techniques in CAGD. Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization. In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensed-matter physics. In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary. Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.
Category: Mathematics

Numerical Methods In Fluid Mechanics

Author : Alain Vincent
ISBN : 0821808133
Genre : Science
File Size : 27.60 MB
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After centuries of research, turbulence in fluids is still an unsolved problem. The graduate-level lectures in this volume cover the state of the art of numerical methods for fluid mechanics. The research in this collection covers wavelet-based methods, the semi-Lagrangian method, the Lagrangian multi-pole method, continuous adaptation of curvilinear grids, finite volume methods, shock-capturing methods, and ENO schemes. The most recent research on large eddy simulations and Reynolds stress modeling is presented in a way that is accessible to engineers, postdoctoral researchers, and graduate students. Applications cover industrial flows, aerodynamics, two-phase flows, astrophysical flows, and meteorology. This volume would be suitable as a textbook for graduate students with a background in fluid mechanics.
Category: Science

Wavelets And Statistics

Author : Anestis Antoniadis
ISBN : 9781461225447
Genre : Mathematics
File Size : 50.24 MB
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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.
Category: Mathematics

Progress In Measurement And Testing

Author : Yanwen Wu
ISBN : 9783038134077
Genre : Technology & Engineering
File Size : 74.56 MB
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The volume consists of a collection of 124 peer-reviewed papers contributed by experts from all over the world. The topics covered include: new developments and applications in materials forming, subtractive, additive and joining processes, processing of advanced materials such as composites, polymers, semiconductors and bio-materials, and new development in the micro/nano-fabrication of engineering materials.
Category: Technology & Engineering

Ripples In Mathematics

Author : A. Jensen
ISBN : 9783642567025
Genre : Mathematics
File Size : 32.51 MB
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This introduction to the discrete wavelet transform and its applications is based on a novel approach to discrete wavelets called lifting. After an elementary introduction, connections of filter theory are presented, and wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals, problems with finite length signals are detailed, and MATLAB is used for examples and implementation of transforms.
Category: Mathematics

Sampling Wavelets And Tomography

Author : John J. Benedetto
ISBN : 0817643044
Genre : Computers
File Size : 67.74 MB
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Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis. The advent of new techniques in mathematical analysis has strengthened their interdependence and led to some new and interesting results in the field. Aimed at mathematicians, scientists, and engineers working in signal and image processing and medical imaging, the work is designed to be accessible to an audience with diverse mathematical backgrounds. Although the volume reflects the contributions of renowned mathematicians and engineers, each chapter has an expository introduction written for the non-specialist. One of the key features of the book is an introductory chapter stressing the interdependence of the three main areas covered. A comprehensive index completes the work.
Category: Computers

Ten Lectures On Wavelets

Author : Ingrid Daubechies
ISBN : 9780898712742
Genre : Science
File Size : 27.31 MB
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Mathematics of Computing -- Miscellaneous.
Category: Science

Multimedia Processing Communication And Computing Applications

Author : Punitha P. Swamy
ISBN : 9788132211433
Genre : Technology & Engineering
File Size : 60.21 MB
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ICMCCA 2012 is the first International Conference on Multimedia Processing, Communication and Computing Applications and the theme of the Conference is chosen as ‘Multimedia Processing and its Applications’. Multimedia processing has been an active research area contributing in many frontiers of today’s science and technology. This book presents peer-reviewed quality papers on multimedia processing, which covers a very broad area of science and technology. The prime objective of the book is to familiarize readers with the latest scientific developments that are taking place in various fields of multimedia processing and is widely used in many disciplines such as Medical Diagnosis, Digital Forensic, Object Recognition, Image and Video Analysis, Robotics, Military, Automotive Industries, Surveillance and Security, Quality Inspection, etc. The book will assist the research community to get the insight of the overlapping works which are being carried out across the globe at many medical hospitals and institutions, defense labs, forensic labs, academic institutions, IT companies and security & surveillance domains. It also discusses latest state-of-the-art research problems and techniques and helps to encourage, motivate and introduce the budding researchers to a larger domain of multimedia.
Category: Technology & Engineering

Introduction To Wavelets And Wavelet Transforms

Author : Sidny Burrus
ISBN : STANFORD:36105019319495
Genre : Mathematics
File Size : 44.41 MB
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Advanced undergraduate and beginning graduate students, faculty, researchers and practitioners in signal processing, telecommunications, and computer science, and applied mathematics. It assumes a background of Fourier series and transforms and of linear algebra and matrix methods. This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.
Category: Mathematics

Icaos 96 12th International Conference On Analysis And Optimization Of Systems

Author : Marie-Odile Berger
ISBN : UOM:39015038108067
Genre : Technology & Engineering
File Size : 85.50 MB
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This volume contains the proceedings of ICAOS '96 the 12th International Conference on Analysis and Optimization of Systems. This conference was co-organized by INRIA and the CEREMADE and was dedicated to Images, Wavelets and PDE's. The aim of the conference was to discuss the impact on image analysis of recent mathematical developments in multiscale analysis, partial differential equations, variational methods and so on. ICAOS '96 provided a forum for image processing researchers and mathematicians to interact and to exchange their technical knowledge and experience, theoretical or practical, in this emerging and exciting domain. The selected papers have been organized according to the following sessions, each session corresponding to a section of the book: 1. Active Contours; 2. Image Enhancement and Restoration, Scale-Spaces; 3. Wavelets; 4. Image Segmentation; 5. Image Restoration; 6. Coding; 7. Applications.
Category: Technology & Engineering

Emerging Research In Electronics Computer Science And Technology

Author : V Sridhar
ISBN : 9788132211570
Genre : Technology & Engineering
File Size : 41.41 MB
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PES College of Engineering is organizing an International Conference on Emerging Research in Electronics, Computer Science and Technology (ICERECT-12) in Mandya and merging the event with Golden Jubilee of the Institute. The Proceedings of the Conference presents high quality, peer reviewed articles from the field of Electronics, Computer Science and Technology. The book is a compilation of research papers from the cutting-edge technologies and it is targeted towards the scientific community actively involved in research activities.
Category: Technology & Engineering

Long Memory Processes

Author : Jan Beran
ISBN : 9783642355127
Genre : Mathematics
File Size : 41.13 MB
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Long-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.
Category: Mathematics