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.

One of the most intriguing problems in video processing is the removal of the redundancy or the compression of a video signal. There are a large number of applications which depend on video compression. Data compression represents the enabling technology behind the multimedia and digital television revolution. In motion compensated lossy video compression the original video sequence is first split into three new sources of information, segmentation, motion and residual error. These three information sources are then quantized, leading to a reduced rate for their representation but also to a distorted reconstructed video sequence. After the decomposition of the original source into segmentation, mo tion and residual error information is decided, the key remaining problem is the allocation of the available bits into these three sources of information. In this monograph a theory is developed which provides a solution to this fundamental bit allocation problem. It can be applied to all quad-tree-based motion com pensated video coders which use a first order differential pulse code modulation (DPCM) scheme for the encoding of the displacement vector field (DVF) and a block-based transform scheme for the encoding of the displaced frame differ ence (DFD). An optimal motion estimator which results in the smallest DFD energy for a given bit rate for the encoding of the DVF is also a result of this theory. Such a motion estimator is used to formulate a motion compensated interpolation scheme which incorporates a global smoothness constraint for the DVF.

This book constitutes the refereed proceedings of the Second International Conference on Wavelet Analysis and Its Applications, WAA 2001, held in Hong Kong, China in December 2001. The 24 revised full papers and 27 revised short papers presented were carefully reviewed and selected from a total of 67 full paper submissions. The book offers topical sections on image compression and coding, video coding and processing, theory, image processing, signal processing, and systems and applications.

The object of this dissertation is to investigate rate-distortion optimization and to evaluate the prospects of adaptive vector quantization for digital video compression. Rate-distortion optimization aims to improve compression performance using discrete optimization algorithms. We first describe and classify algorithms that have been developed in the literature to date. One algorithms is extended in order to make it generally applicable; the correctness of this new procedure is proven. Moreover, we compare the complexity of the aforesaid algorithms, first implementation-independent and then by run-time experiments. Finally, we propose a technique to speed up one of the aforementioned algorithms. Adaptive vector quantization enables adaption to sources with unknown or non-stationary statistics. This feature is important for digital video data since the statistics of two subsequent frames is usually similar, but in the long run the general statistics of frames may change even if scene changes are neglected. We examine combinations of adaptive vector quantization with various state-of-the-art video compression techniques. First we present an adaptive vector quantization based codec that is able to encode and decode in real-time using current PC technology. This codec is rate-distortion optimized and adaptive vector quantization is applied in the wavelet transform domain. The organization of the wavelet coefficients is then made more efficient using adaptive partition techniques. Moreover, the main adaptability mechanism of adaptive vector quantization, the so-called codebook update, is studied. Finally, a combination of adaptive vector quantization and motion compensation is taken into consideration. We show that for very low bitrates adaptive vector quantization performs on prediction residual frames better or at least as well as discrete cosine transform coding.

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