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Author: Lokenath Debnath Publisher: Springer ISBN: 0817684182 Category : Technology & Engineering Languages : en Pages : 562
Book Description
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.
Author: Lokenath Debnath Publisher: Springer ISBN: 0817684182 Category : Technology & Engineering Languages : en Pages : 562
Book Description
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.
Author: Inderpreet Singh Publisher: ISBN: Category : Languages : en Pages :
Book Description
With the evolution of multimedia systems, image and video compression is becoming the key enabling technology for delivering various image/video services over heterogeneous networks. The basic goal of image data compression is to reduce the bit rate for transmission and storage while either maintaining the original quality of the data or providing an acceptable quality. This thesis proposes a new wavelet transform for lossless compression of images with application to medical images. The transform uses integer arithmetic and is very computationally efficient. Then a new color image transformation, which is reversible and uses integer arithmetic, is proposed. The transformation reduces the redundancy among the red, green, and blue color bands. It approximates the luminance and chrominance components of the YIQ coordinate system. This transformation involves no floating point/integer multiplications or divisions, and is, therefore, very suitable for real-time applications where the number of CPU cycles needs to be kept to a minimum. A technique for lossy compression of an image data base is also proposed. The technique uses a wavelet transform and vector quantization for compression. The discrete cosine transform is applied to the coarsest scale wavelet coefficients to achieve even higher compression ratios without any significant increase in computational complexity. Wavelet denoising is used to reduce the image artifacts generated by quantizing the discrete cosine transform coefficients. This improves the subjective quality of the decompressed images for very low bit rate images (less than 0.5 bits per pixel). The thesis also deals with the real-time implementation of the wavelet transform. The new wavelet transform has been applied to speech signals. Both lossless and lossy techniques for speech coding have been implemented. The lossless technique involves using the reversible integer-arithmetic wavelet transform and Huffman coding to obtain the compressed bitstream. The lossy technique, on the other hand, quantizes the wavelet coefficients to obtain higher compression ratio at the expense of some degradation in sound quality. The issues related to real-time wavelet compression are also discussed. Due to the limited size of memory on a DSP, a wavelet transform had to be applied to an input signal of finite length. The effects of varying the signal length on compression performance are also studied for different reversible wavelet transforms. The limitations of the proposed techniques are discussed and recommendations for future research are provided.
Author: Patrick J. Van Fleet Publisher: John Wiley & Sons ISBN: 1118030664 Category : Mathematics Languages : en Pages : 570
Book Description
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.
Author: A. K. Louis Publisher: Wiley ISBN: 9780471967927 Category : Mathematics Languages : en Pages : 342
Book Description
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.
Author: Patrick J. Van Fleet Publisher: John Wiley & Sons ISBN: 1118979273 Category : Mathematics Languages : en Pages : 637
Book Description
Updated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals The new edition of Discrete Wavelet Transformations continues to guide readers through the abstract concepts of wavelet theory by using Dr. Van Fleet’s highly practical, application-based approach, which reflects how mathematicians construct solutions to challenges outside the classroom. By introducing the Haar, orthogonal, and biorthogonal filters without the use of Fourier series, Van Fleet allows his audience to connect concepts directly to real-world applications at an earlier point than other publications in the field. Leveraging extensive graphical displays, this self-contained volume integrates concepts from calculus and linear algebra into the constructions of wavelet transformations and their applications, including data compression, edge detection in images and denoising of signals. Conceptual understanding is reinforced with over 500 detailed exercises and 24 computer labs. The second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include: Two new chapters covering wavelet packets and the lifting method A reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques A new comprehensive chapter that explains filter derivation using Fourier techniques Over 120 examples of which 91 are “live examples,” which allow the reader to quickly reproduce these examples in Mathematica or MATLAB and deepen conceptual mastery An overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented A complete rewrite of the DiscreteWavelets package called WaveletWare for use with Mathematica and MATLAB A website, www.stthomas.edu/wavelets, featuring material containing the WaveletWare package, live examples, and computer labs in addition to companion material for teaching a course using the book Comprehensive and grounded, this book and its online components provide an excellent foundation for developing undergraduate courses as well as a valuable resource for mathematicians, signal process engineers, and other professionals seeking to understand the practical applications of discrete wavelet transformations in solving real-world challenges.
Author: Kamisetty Ramam Rao Publisher: CRC Press ISBN: 1420037382 Category : Computers Languages : en Pages : 408
Book Description
Data compression is one of the main contributing factors in the explosive growth in information technology. Without it, a number of consumer and commercial products, such as DVD, videophone, digital camera, MP3, video-streaming and wireless PCS, would have been virtually impossible. Transforming the data to a frequency or other domain enables even more efficient compression. By illustrating this intimate link, The Transform and Data Compression Handbook serves as a much-needed handbook for a wide range of researchers and engineers. The authors describe various discrete transforms and their applications in different disciplines. They cover techniques, such as adaptive quantization and entropy coding, that result in significant reduction in bit rates when applied to the transform coefficients. With clear and concise presentations of the ideas and concepts, as well as detailed descriptions of the algorithms, the authors provide important insight into the applications and their limitations. Data compression is an essential step towards the efficient storage and transmission of information. The Transform and Data Compression Handbook provides a wealth of information regarding different discrete transforms and demonstrates their power and practicality in data compression.
Author: Stephane Jaffard Publisher: SIAM ISBN: 9780898718119 Category : Mathematics Languages : en Pages : 258
Book Description
This long-awaited update of Meyer's Wavelets : algorithms and applications includes completely new chapters on four topics: wavelets and the study of turbulence, wavelets and fractals (which includes an analysis of Riemann's nondifferentiable function), data compression, and wavelets in astronomy. The chapter on data compression was the original motivation for this revised edition, and it contains up-to-date information on the interplay between wavelets and nonlinear approximation. The other chapters have been rewritten with comments, references, historical notes, and new material. Four appendices have been added: a primer on filters, key results (with proofs) about the wavelet transform, a complete discussion of a counterexample to the Marr-Mallat conjecture on zero-crossings, and a brief introduction to Hölder and Besov spaces. In addition, all of the figures have been redrawn, and the references have been expanded to a comprehensive list of over 260 entries. The book includes several new results that have not appeared elsewhere.
Author: Hannu Olkkonen Publisher: BoD – Books on Demand ISBN: 9533074825 Category : Computers Languages : en Pages : 312
Book Description
The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications.
Author: Lokenath Debnath
Author: 
Author: Lokenath Debnath
Author: Inderpreet Singh
Author: Patrick J. Van Fleet
Author: A. K. Louis
Author: Patrick J. Van Fleet
Author: Kamisetty Ramam Rao
Author: 
Author: Stephane Jaffard
Author: Hannu Olkkonen