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Wavelet Transforms And Their Applications

Author : Lokenath Debnath
ISBN : 9780817684181
Genre : Technology & Engineering
File Size : 62. 70 MB
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This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.

A Primer On Wavelets And Their Scientific Applications

Author : James S. Walker
ISBN : 142005001X
Genre : Mathematics
File Size : 51. 24 MB
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The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques. Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data. Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABä. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned. Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.

Wavelets And Their Applications

Author : J.S. Byrnes
ISBN : 0792330781
Genre : Mathematics
File Size : 25. 59 MB
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It is probably true quite generally that in the history of human thinking the most fruitful developments frequently take place at those points where two different lines of thought meet. Hence, if they actually meet, that is, if they are at least so much related to each other that a real interaction can take place, then one may hope that new and interesting developments may follow. Werner Heisenberg This volume contains papers presented at the August 1992 NATO Advanced Study Institute on Wavelets and Their Applications. The conference was held at the beautiful Il Ciocco resort near Lucca, in the glorious Tuscany region of northern Italy. Once again we gathered at this idyllic spot to explore and extend the reciprocity between mathematics and engineering. The dynamic interaction between world-renowned scientists from the usu ally disparate communities of pure mathematicians and applied scientists, which occurred at our 1989 and 1991 ASI's, continued at this meeting. Wavelet theory and technology is in an important growth stage at which theoretical and practical results are being compared with existing methods. There have been spectacular wavelet successes and sobering comparisons with traditional ideas-but still there is a wide expanse of scientific problems to explore. Since these problems lie at the forefront of both pure mathematics and applied science, our NATO ASI was especially pertinent at this time.

Wavelets And Their Applications

Author : Mei Kobayashi
ISBN : 9780898714166
Genre : Mathematics
File Size : 38. 19 MB
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This collection of independent case studies demonstrates how wavelet techniques have been used to solve open problems and develop insight into the nature of the systems under study. Each case begins with a description of the problem and points to the specific properties of wavelets and techniques used for determining a solution. The cases range from a very simple wavelet-based technique for reducing noise in laboratory data to complex work on two-dimensional geographical data display conducted at the Earthquake Research Institute in Japan. One case study shows how wavelet analysis is used in the development of a Japanese text-to-speech system for personal computers and another presents new wavelet techniques developed for and applied to the study of atmospheric wind, turbulent fluid, and seismic acceleration data.

Wavelets And Their Applications

Author : Michel Misiti
ISBN : 9781118613597
Genre : Technology & Engineering
File Size : 67. 28 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.

Fractals Wavelets And Their Applications

Author : Christoph Bandt
ISBN : 9783319081052
Genre : Mathematics
File Size : 26. 22 MB
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Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.

Wavelets Multiwavelets And Their Applications

Author : Akram Aldroubi
ISBN : 0821855522
Genre : Mathematics
File Size : 75. 1 MB
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This volume contains refereed research articles on the active area of wavelets and multi-wavelets. The book draws upon work presented by experts in the field during the special session on "Wavelets, Multiwavelets and Their Applications" at the Joint Mathematics Meetings in San Diego (January 1997). Wavelets were implicit in mathematics, physics, signal or image processing, and numerical analysis long before they were given the status of a unified scientific field in the late 1980s. They continue to be one of the few subjects that have attracted considerable interest from the mathematical community as well as from other diverse disciplines where they have promising applications. The topic is in full evolution, with many active research efforts emerging from the fruitful interaction of various mathematical subjects and other scientific disciplines.

Wavelets

Author : John J. Benedetto
ISBN : 0849382718
Genre : Mathematics
File Size : 38. 45 MB
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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.

Wavelet Theory And Its Applications

Author : Randy K. Young
ISBN : 079239271X
Genre : Technology & Engineering
File Size : 55. 64 MB
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The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.

Wavelets In Medicine And Biology

Author : Akram Aldroubi
ISBN : 084939483X
Genre : Mathematics
File Size : 37. 20 MB
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Considerable attention from the international scientific community is currently focused on the wide ranging applications of wavelets. For the first time, the field's leading experts have come together to produce a complete guide to wavelet transform applications in medicine and biology. Wavelets in Medicine and Biology provides accessible, detailed, and comprehensive guidelines for all those interested in learning about wavelets and their applications to biomedical problems.

Adaptive Wavelets And Their Applications To Image Fusion And Compression

Author : Gema Piella
ISBN : OCLC:66395451
Genre :
File Size : 66. 77 MB
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Wavelet Theory

Author : David K. Ruch
ISBN : 9781118165669
Genre : Mathematics
File Size : 62. 41 MB
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A self-contained, elementary introduction to wavelet theory andapplications Exploring the growing relevance of wavelets in the field ofmathematics, Wavelet Theory: An Elementary Approach withApplications provides an introduction to the topic, detailing thefundamental concepts and presenting its major impacts in the worldbeyond academia. Drawing on concepts from calculus and linearalgebra, this book helps readers sharpen their mathematical proofwriting and reading skills through interesting, real-worldapplications. The book begins with a brief introduction to the fundamentals ofcomplex numbers and the space of square-integrable functions. Next,Fourier series and the Fourier transform are presented as tools forunderstanding wavelet analysis and the study of wavelets in thetransform domain. Subsequent chapters provide a comprehensivetreatment of various types of wavelets and their related concepts,such as Haar spaces, multiresolution analysis, Daubechies wavelets,and biorthogonal wavelets. In addition, the authors include twochapters that carefully detail the transition from wavelet theoryto the discrete wavelet transformations. To illustrate therelevance of wavelet theory in the digital age, the book includestwo in-depth sections on current applications: the FBI WaveletScalar Quantization Standard and image segmentation. In order to facilitate mastery of the content, the book featuresmore than 400 exercises that range from theoretical tocomputational in nature and are structured in a multi-part formatin order to assist readers with the correct proof or solution.These problems provide an opportunity for readers to furtherinvestigate various applications of wavelets. All problems arecompatible with software packages and computer labs that areavailable on the book's related Web site, allowing readers toperform various imaging/audio tasks, explore computer wavelettransformations and their inverses, and visualize the applicationsdiscussed throughout the book. Requiring only a prerequisite knowledge of linear algebra andcalculus, Wavelet Theory is an excellent book for courses inmathematics, engineering, and physics at the upper-undergraduatelevel. It is also a valuable resource for mathematicians,engineers, and scientists who wish to learn about wavelet theory onan elementary level.

A Primer On Wavelets And Their Scientific Applications Second Edition

Author : James S. Walker
ISBN : 1584887451
Genre : Mathematics
File Size : 87. 12 MB
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In the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include the latest developments, this second edition of A Primer on Wavelets and Their Scientific Applications guides readers through the main ideas of wavelet analysis in order to develop a thorough appreciation of wavelet applications. Ingeniously relying on elementary algebra and just a smidgen of calculus, Professor Walker demonstrates how the underlying ideas behind wavelet analysis can be applied to solve significant problems in audio and image processing, as well in biology and medicine. Nearly twice as long as the original, this new edition provides · 104 worked examples and 222 exercises, constituting a veritable book of review material · Two sections on biorthogonal wavelets · A mini-course on image compression, including a tutorial on arithmetic compression · Extensive material on image denoising, featuring a rarely covered technique for removing isolated, randomly positioned clutter · Concise yet complete coverage of the fundamentals of time-frequency analysis, showcasing its application to audio denoising, and musical theory and synthesis · An introduction to the multiresolution principle, a new mathematical concept in musical theory · Expanded suggestions for research projects · An enhanced list of references · FAWAV: software designed by the author, which allows readers to duplicate described applications and experiment with other ideas. To keep the book current, Professor Walker has created a supplementary website. This online repository includes ready-to-download software, and sound and image files, as well as access to many of the most important papers in the field.

Digital Signal Processing Using Matlab And Wavelets

Author : Michael Weeks
ISBN : 9780977858200
Genre : Computers
File Size : 28. 72 MB
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With emphasis on the practical applications of signal processing, this book is designed for upper division engineering & computer sciences students as well as practicing engineers.

Wavelets And Operators Volume 1

Author : Yves Meyer
ISBN : 0521458692
Genre : Mathematics
File Size : 61. 29 MB
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The definite mathematical treatment of this important area, written by one of the founders of the field.

A First Course On Wavelets

Author : Eugenio Hernandez
ISBN : 1420049984
Genre : Mathematics
File Size : 25. 30 MB
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Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: Several bases generated by a single function via translations and dilations Multiresolution analysis, compactly supported wavelets, and spline wavelets Band-limited wavelets Unconditionality of wavelet bases Characterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided, and constructions of splines wavelets are presented. Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.

Wavelets And Their Applications

Author : Et Al Ruskai
ISBN : UOM:39015049377578
Genre : Mathematics
File Size : 73. 8 MB
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Contributions discuss signal analysis discrete-time signal processing, wavelets for Quincunx pyramid, transform maxima and multiscale edges, among other topics; numerical analysis; other applications the optical wave transform, continuous wavelet transform, quantum mechanics; and theoretical develop

Discrete Wavelet Transformations

Author : Patrick J. Van Fleet
ISBN : 9781118030660
Genre : Mathematics
File Size : 84. 43 MB
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An "applications first" approach to discrete wavelettransformations Discrete Wavelet Transformations provides readers with a broadelementary introduction to discrete wavelet transformations andtheir applications. With extensive graphical displays, thisself-contained book integrates concepts from calculus and linearalgebra into the construction of wavelet transformations and theirvarious applications, including data compression, edge detection inimages, and signal and image denoising. The book begins with a cursory look at wavelet transformationdevelopment and illustrates its allure in digital signal and imageapplications. Next, a chapter on digital image basics, quantitativeand qualitative measures, and Huffman coding equips readers withthe tools necessary to develop a comprehensive understanding of theapplications. Subsequent chapters discuss the Fourier series,convolution, and filtering, as well as the Haar wavelet transformto introduce image compression and image edge detection. Thedevelopment of Daubechies filtersis presented in addition tocoverage of wavelet shrinkage in the area of image and signaldenoising. The book concludes with the construction of biorthogonalfilters and also describes their incorporation in the JPEG2000image compression standard. The author's "applications first" approach promotes a hands-ontreatment of wavelet transforma-tion construction, and over 400exercises are presented in a multi-part format that guide readersthrough the solution to each problem. Over sixty computer labs andsoftware development projects provide opportunities for readers towrite modules and experiment with the ideas discussed throughoutthe text. The author's software package, DiscreteWavelets, is usedto perform various imaging and audio tasks, compute wavelettransformations and inverses, and visualize the output of thecomputations. Supplementary material is also available via thebook's related Web site, which includes an audio and videorepository, final project modules, and softwarefor reproducingexamples from the book. All software, including theDiscreteWavelets package, is available for use withMathematica®, MATLAB®, and Maple. Discrete Wavelet Transformations strongly reinforces the use ofmathematics in digital data applications, sharpens programmingskills, and provides a foundation for further study of moreadvanced topics, such as real analysis. This book is ideal forcourses on discrete wavelet transforms and their applications atthe undergraduate level and also serves as an excellent referencefor mathematicians, engineers, and scientists who wish to learnabout discrete wavelet transforms at an elementary level.

Digital Signal Processing Using Matlab Wavelets

Author : Michael Weeks
ISBN : 9780763784225
Genre : Computers
File Size : 88. 13 MB
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Although Digital Signal Processing (DSP) has long been considered an electrical engineering topic, recent developments have also generated significant interest from the computer science community. DSP applications in the consumer market, such as bioinformatics, the MP3 audio format, and MPEG-based cable/satellite television have fueled a desire to understand this technology outside of hardware circles. Designed for upper division engineering and computer science students as well as practicing engineers and scientists, Digital Signal Processing Using MATLAB & Wavelets, Second Edition emphasizes the practical applications of signal processing. Over 100 MATLAB examples and wavelet techniques provide the latest applications of DSP, including image processing, games, filters, transforms, networking, parallel processing, and sound. This Second Edition also provides the mathematical processes and techniques needed to ensure an understanding of DSP theory. Designed to be incremental in difficulty, the book will benefit readers who are unfamiliar with complex mathematical topics or those limited in programming experience. Beginning with an introduction to MATLAB programming, it moves through filters, sinusoids, sampling, the Fourier transform, the z-transform and other key topics. Two chapters are dedicated to the discussion of wavelets and their applications. A CD-ROM (platform independent) accompanies the book and contains source code, projects for each chapter, and the figures from the book.

Wavelets For Computer Graphics

Author : Eric J. Stollnitz
ISBN : 1558603751
Genre : Computers
File Size : 25. 58 MB
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This introduction to wavelets provides computer graphics professionals and researchers with the mathematical foundations for understanding and applying this powerful tool.

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