Wavelets In Image Communication

The rapid advancements in image communication technologies are documented in the book series, Advances in Image Communication. Each publication provides an in-depth exploration of an intrinsic element of the multi-disciplinary field and together they form a comprehensive overview of the whole. This volume, the fifth in the series, examines the definition, study and use of the wavelet transform in communications for two-dimensional (2-D) digital signals. The transform is used for signal reorganization before compression and the trade-off between these two steps and the whole compression process is discussed. The five chapters specifically present the theory of wavelets applied to images, then applications of compression of still images and sequences. Chapter 1 introduces biorthogonal bases of compactly supported wavelets: this generalization of orthonormal wavelet theory allows the use of linear phase filters. A non rectangular wavelet representation of 2-D signals is developed in the second chapter: the properties usually used with wavelets, phase, linearity, and regularity are discussed. Chapter 3 is composed of three parts: a description of commonly used biorthogonal wavelets; a presentation of vector quantization algorithms; a consideration of lattice vector quantization followed by a discussion of the bit allocation procedure (with experimental results given). The fourth chapter deals with a region-based discrete wavelet transform for image coding. Chapter 5 investigates the transmission of image sequences: wavelet transforms and motion estimation are detailed in a multiconstraint approach of image sequence coding.

The past few years have seen a rapid growth in image processing and image communication technologies. New video services and multimedia applications are continuously being designed. Essential for all these applications are image and video compression techniques. The purpose of this book is to report on recent advances in VLSI architectures and their implementation for video signal processing applications with emphasis on video coding for bit rate reduction. Efficient VLSI implementation for video signal processing spans a broad range of disciplines involving algorithms, architectures, circuits, and systems. Recent progress in VLSI architectures and implementations has resulted in the reduction in cost and size of video signal processing equipment and has made video applications more practical. The topics covered in this volume demonstrate the increasingly interdisciplinary nature of VLSI implementation of video signal processing applications, involving interactions between algorithms, VLSI architectures, circuit techniques, semiconductor technologies and CAD for microelectronics.

Discusses recent advances in the related technologies of multimedia computers, videophones, video-over-Internet, HDTV, digital satellite TV and interactive computer games. The text analyzes ways of achieving more effective navigation techniques, data management functions, and higher throughout networking. It synthesizes data on visual information venues, tracking the enormous commercial potential for new components and compatible systems.

Despite their novelty, wavelets have a tremendous impact on a number of modern scientific disciplines, particularly on signal and image analysis. Because of their powerful underlying mathematical theory, they offer exciting opportunities for the design of new multi-resolution processing algorithms and effective pattern recognition systems. This book provides a much-needed overview of current trends in the practical application of wavelet theory. It combines cutting edge research in the rapidly developing wavelet theory with ideas from practical signal and image analysis fields. Subjects dealt with include balanced discussions on wavelet theory and its specific application in diverse fields, ranging from data compression to seismic equipment. In addition, the book offers insights into recent advances in emerging topics such as double density DWT, multiscale Bayesian estimation, symmetry and locality in image representation, and image fusion. Audience: This volume will be of interest to graduate students and researchers whose work involves acoustics, speech, signal and image processing, approximations and expansions, Fourier analysis, and medical imaging.

This book is intended for use in the teaching of graduate and senior undergraduate courses on multiresolution signal and geometry processing in the engineering and related disciplines. It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been well received by students. This book provides a comprehensive introduction to multiresolution signal and geometry processing, with a focus on both theory and applications. The book has two main components, corresponding to multiresolution processing in the contexts of: 1) signal processing and 2) geometry processing. The signal-processing component of the book studies one-dimensional and multi-dimensional multirate systems, considering multirate structures such as sampling-rate converters, filter banks, and transmultiplexers. A particularly strong emphasis is placed on filter banks. Univariate and multivariate wavelet systems are examined, with the biorthogonal and orthonormal cases both being considered. The relationship between filter banks and wavelet systems is established. Several applications of filter banks and wavelets in signal processing are covered, including signal coding, image compression, and noise reduction. For readers interested in image compression, a detailed overview of the JPEG-2000 standard is also provided. Some other applications of multirate systems are considered, such as transmultiplexers for communication systems (e.g., multicarrier modulation). The geometry-processing component of the book studies subdivision surfaces and subdivision wavelets. Some mathematical background relating to geometry processing is provided, including topics such as homogeneous coordinate transformations, manifolds, surface representations, and polygon meshes. Several subdivision schemes are examined in detail, including the Loop, Kobbelt sqrt(3), and Catmull-Clark methods. The application of subdivision surfaces in computer graphics is considered. A detailed introduction to functional analysis is provided, for those who would like a deeper understanding of the mathematics underlying wavelets and filter banks. For those who are interested in software applications of the material covered in the book, appendices are included that introduce the CGAL and OpenGL libraries. Also, an appendix on the SPL library (which was developed for use with this book) is included. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.

An exciting new development has taken place in the digital era that has captured the imagination and talent of researchers around the globe - wavelet image compression. This technology has deep roots in theories of vision, and promises performance improvements over all other compression methods, such as those based on Fourier transforms, vectors quantizers, fractals, neural nets, and many others. It is this revolutionary new technology that is presented in Wavelet Image and Video Compression, in a form that is accessible to the largest audience possible. Wavelet Image and Video Compression is divided into four parts. Part I, Background Material, introduces the basic mathematical structures that underly image compression algorithms with the intention of providing an easy introduction to the mathematical concepts that are prerequisites for the remainder of the book. It explains such topics as change of bases, scalar and vector quantization, bit allocation and rate-distortion theory, entropy coding, the discrete-cosine transform, wavelet filters and other related topics. Part II, Still Image Coding, presents a spectrum of wavelet still image coding techniques. Part III, Special Topics in Still Image Coding, provides a variety of example coding schemes with a special flavor in either approach or application domain. Part IV, Video Coding, examines wavelet and pyramidal coding techniques for video data. Wavelet Image and Video Compression serves as an excellent reference and may be used as a text for advanced courses covering the subject.

A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.

Despite their novelty, wavelets have a tremendous impact on a number of modern scientific disciplines, particularly on signal and image analysis. Because of their powerful underlying mathematical theory, they offer exciting opportunities for the design of new multi-resolution processing algorithms and effective pattern recognition systems. This book provides a much-needed overview of current trends in the practical application of wavelet theory. It combines cutting edge research in the rapidly developing wavelet theory with ideas from practical signal and image analysis fields. Subjects dealt with include balanced discussions on wavelet theory and its specific application in diverse fields, ranging from data compression to seismic equipment. In addition, the book offers insights into recent advances in emerging topics such as double density DWT, multiscale Bayesian estimation, symmetry and locality in image representation, and image fusion. Audience: This volume will be of interest to graduate students and researchers whose work involves acoustics, speech, signal and image processing, approximations and expansions, Fourier analysis, and medical imaging.