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.

This book explains the stages necessary to create a wavelet compression system for images and describes state-of-the-art systems used in image compression standards and current research. It starts with a high level discussion of the properties of the wavelet transform, especially the decomposition into multi-resolution subbands. It continues with an exposition of the null-zone, uniform quantization used in most subband coding systems and the optimal allocation of bitrate to the different subbands. Then the image compression systems of the FBI Fingerprint Compression Standard and the JPEG2000 Standard are described in detail. Following that, the set partitioning coders SPECK and SPIHT, and EZW are explained in detail and compared via a fictitious wavelet transform in actions and number of bits coded in a single pass in the top bit plane. The presentation teaches that, besides producing efficient compression, these coding systems, except for the FBI Standard, are capable of writing bit streams that have attributes of rate scalability, resolution scalability, and random access decoding. Many diagrams and tables accompany the text to aid understanding. The book is generous in pointing out references and resources to help the reader who wishes to expand his knowledge, know the origins of the methods, or find resources for running the various algorithms or building his own coding system. Table of Contents: Introduction / Characteristics of the Wavelet Transform / Generic Wavelet-based Coding Systems / The FBI Fingerprint Image Compression Standard / Set Partition Embedded Block (SPECK) Coding / Tree-based Wavelet Transform Coding Systems / Rate Control for Embedded Block Coders / Conclusion

Sixth in the book series, Advances in Image Communication, which documents the rapid advancements of recent years in image communication technologies, this volume provides a comprehensive exploration of subband coding.Originally, subband coding and transform coding were developed separately. The former, however, benefitted considerably from the earlier evolution of transform coding theory and practice. Retaining their own terminology and views, the two methods are closely related and this book indeed aims to unify the approaches. Specifically, the volume contributes effectively to the understanding of frequency domain coding techniques. Many images from coding experiments are presented, enabling the reader to consider the properties of different coders.Chapter 1 introduces the problem of image compression in general terms. Sampling of images and other fundamental concepts, such as entropy and the rate distortion function, are briefly reviewed. The idea of viewing coding techniques as series expansions is also introduced. The second chapter presents signal decomposition and the conditions for perfect reconstruction from minimum representations. Chapter 3 deals with filter bank structures, primarily those displaying the perfect reconstruction property. Quantization techniques and the efficient exploitation of the bit resources are discussed from a theoretical perspective in Chapter 4 and this issue is further examined in Chapter 6, from a more practical point of view. Chapter 5 provides a development of gain formulas, i.e. quantitative measures of the performance of filter banks in a subband coding context, and these are then employed in a search for optimal filter banks. A number of examples of coded images using different subband coders are presented in Chapter 7, these indicating that subband coders give rise to some characteristic types of image degradations. Accordingly, Chapter 8 presents several techniques for minimizing these artifacts. The theory and practice of subband coding of video, at several target bit rates, is discussed in the last chapter.

The scientists and engineers of today are relentless in their continuing study and analysis of the world about us from the microcosm to the macrocosm. A central purpose of this study is to gain sufficient scientific information and insight to enable the development of both representative and useful models of the superabundance of physical processes that surround us. The engineers need these models and the associated insight in order to build the information processing systems and control systems that comprise these new and emerging technologies. Much of the early modeling work that has been done on these systems has been based on the linear time-invariant system theory and its extensive use of Fourier transform theory for both continuous and discrete systems and signals. However many of the signals arising in nature and real systems are neither stationary nor linear but tend to be concentrated in both time and frequency. Hence a new methodology is needed to take these factors properly into account.