Motivated by the Markov Chain Monte Carlo (MCMC) approach to the compression of discrete sources developed by Jalali and Weissman, we propose a lossy compression algorithm for analog sources that relies on a finite reproduction alphabet, which grows with the input length. The algorithm achieves, in an appropriate asymptotic sense, the optimum Shannon theoretic tradeoff between rate and distortion, universally for stationary ergodic continuous amplitude sources. We further propose an MCMC-based algorithm that resorts to a reduced reproduction alphabet when such reduction does not prevent achieving the Shannon limit. The latter algorithm is advantageous due to its reduced complexity and improved rates of convergence when employed on sources with a finite and small optimum reproduction alphabet.
H.264 AVC is newest video coding standard of the ITU-T Video Coding Experts Group and the ISO IEC Moving Picture Experts Group. The main goals of the H.264 AVC standardization effort have been enhanced compression performance and provision of a "network-friendly" video representation addressing "conversational" (video telephony) and "nonconversational" (storage, broadcast, or streaming) applications. H.264 AVC has achieved a significant improvement in rate-distortion efficiency relative to existing standards. This article provides an overview of the technical features of H.264 AVC, describes profiles and applications for the standard, and outlines the history of the standardization process. This correspondence analyzes the low-resolution performance of entropy-constrained scalar quantization. It focuses mostly on Gaussian sources, for which it is shown that for both binary quantizers and infinite-level uniform threshold quantizers, as D approaches the source variance spl sigma sup 2 , the least entropy of such quantizers with mean-squared error D or less approaches zero with slope -log sub 2 e 2 spl sigma sup 2 . As the Shannon rate-distortion function approaches zero with the same slope, this shows that in the low-resolution region, scalar quantization with entropy coding is asymptotically as good as any coding technique. We introduce a new image compression paradigm that combines compression efficiency with speed, and is based on an independent "infinite" mixture model which accurately captures the space-frequency characterization of the wavelet image representation. Specifically, we model image wavelet coefficients as being drawn from an independent generalized Gaussian distribution field, of fixed unknown shape for each subband, having zero mean and unknown slowly spatially-varying variances. Based on this model, we develop a powerful "on the fly" estimation-quantization (EQ) framework that consists of: (i) first finding the maximum-likelihood estimate of the individual spatially-varying coefficient field variances based on causal and quantized spatial neighborhood contexts; and (ii) then applying an off-line rate-distortion (R-D) optimized quantization entropy coding strategy, implemented as a fast lookup table, that is optimally matched to the derived variance estimates. A distinctive feature of our paradigm is the dynamic switching between forward and backward adaptation modes based on the reliability of causal prediction contexts. The performance of our coder is extremely competitive with the best published results in the literature across diverse classes of images and target bitrates of interest, in both compression efficiency and processing speed. For example, our coder exceeds the objective performance of the best zerotree-based wavelet coder based on space-frequency-quantization at all bit rates for all tested images at a fraction of its complexity. A new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree-structured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out tree-structured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all nonzeroed coefficients), and we formalize the problem of optimizing their joint application. We develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive, often outperforming the very best coding algorithms in the literature. Quantization, the process of approximating continuous-amplitude signals by digital (discrete-amplitude) signals, is an important aspect of data compression or coding, the field concerned with the reduction of the number of bits necessary to transmit or store analog data, subject to a distortion or fidelity criterion. The independent quantization of each signal value or parameter is termed scalar quantization, while the joint quantization of a block of parameters is termed block or vector quantization. This tutorial review presents the basic concepts employed in vector quantization and gives a realistic assessment of its benefits and costs when compared to scalar quantization. Vector quantization is presented as a process of redundancy removal that makes effective use of four interrelated properties of vector parameters: linear dependency (correlation), nonlinear dependency, shape of the probability density function (pdf), and vector dimensionality itself. In contrast, scalar quantization can utilize effectively only linear dependency and pdf shape. The basic concepts are illustrated by means of simple examples and the theoretical limits of vector quantizer performance are reviewed, based on results from rate-distortion theory. Practical issues relating to quantizer design, implementation, and performance in actual applications are explored. While many of the methods presented are quite general and can be used for the coding of arbitrary signals, this paper focuses primarily on the coding of speech signals and parameters.