Subband Image Coding

This book concerns a new method of image data compression which weil may supplant the well-established block-transfonn methods that have been state-of-the art for the last 15 years. Subband image coding or SBC was first perfonned as such in 1985, and as the results became known at first through conference proceedings, and later through journal papers, the research community became excited about both the theoretical and practical aspects of this new approach. This excitement is continuing today, with many major research laboratories and research universities around the world investigating the subband approach to coding of color images, high resolution images, video- including video conferencing and advanced tele vision, and the medical application of picture archiving systems. Much of the fruits of this work is summarized in the eight chapters of this book which were written by leading practitioners in this field. The subband approach to image coding starts by passing the image through a two- or three-dimensional filter bank. The two-dimensional (2-D) case usually is hierarchical' consisting of two stages of four filters each. Thus the original image is split into 16 subband images, with each one decimated or subsampled by 4x4, resulting in a data conservation. The individual channel data is then quantized ·for digital transmission. In an attractive variation an octave-like approach, herein tenned subband pyramid, is taken for the decomposition resulting in a total of just eleven subbands.

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.

A central goal of signal processing is to describe real-time signals, be it for computation, compression, or understanding. This book presents a unified view of wavelets and subband coding with a signal processing perspective. Covers the discrete-time case, or filter banks; development of wavelets; continuous wavelet and local Fourier transforms; efficient algorithms for filter banks and wavelet computations; and signal compression. *provides broad coverage of theory and applications and a different perspective based on signal processing. *gives framework for applications in speech, audio, image and video compression as used in multimedia. *includes sufficient background material so that people without signal processing knowledge will find it useful.

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.