The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analog-to-digital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first high-resolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analog-to-digital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.

We address the problem of distributed source coding, i.e. compression of correlated sources that are not co-located and/or cannot communicate with each other to minimize their joint description cost. In this work we tackle the related problem of compressing a source that is correlated with another source which is however available only at the decoder. In contrast to prior information-theoretic approaches, we introduce a new constructive and practical framework for tackling the problem based on the judicious incorporation of channel coding principles into this source coding problem. We dub our approach as DIstributed Source Coding Using Syndromes (DISCUS). We focus in this paper on trellis-structured consructions of the framework to illustrate its utility. Simulation results confirm the power of DISCUS, opening up a new and exciting constructive playing-ground for the distributed source coding problem. For the distributed coding of correlated i.i.d. Gaussian sources that are ...

Recently, 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 [1, 2]. 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 non-zeroed coefficients), and we formalize the problem of optimizing their joint application and 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...

Abstract- We present several results regarding the properties of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. We find that for the optimal lattice quantizers this noise is wide-sense-stationary and white. Any desirable noise spectra may be realized by an appropriate linear transformation (“shaping”) of a lattice quantizer. As the dimension increases, the normalized second.moment of the optimal lattice quantizer goes to 1/2xe, and consequently the quantization noise approaches a white Gaussian process in the divergence sense. In entropy-coded dithered quantization, which can be modeled accurately as passing the source through an additive noise channel, this limit behavior implies that for large lattice dimension both the error and the bit rate approach the error and the information rate of an Additive White Gaussian Noise (AWGN) channel. Index Terms-Lattice, quantization noise, shaping, normalized second moment, divergence from Gaussianity. I I.

In 1996, the JPEGcommittee began to investigate possibilities for a new still image compression standard to serve current and future applications. This initiative, which was named JPEG2000, has resulted in a comprehensive standard (ISO 154447ITU-T Recommendation T.800) that is being issued in six parts. Part 1, in the same vein as the JPEG baseline system, is aimed at minimal complexity and maximal interchange and was issued as an International Standard at the end of 2000. Parts 2–6 define extensions to both the compression technology and the file format and are currently in various stages of development. In this paper, a technical description of Part 1 of the JPEG2000 standard is provided, and the rationale behind the selected technologies is explained. Although the JPEG2000 standard only specifies the decoder and the codesteam syntax, the discussion will span both encoder and decoder issues to provide a better

We address the problem of distributed source coding using a practical and constructive approach [1], referred to as Distributed source coding using syndromes (DISCUS), with applications to sensor networks. We propose low complexity encoding and decoding methods based on linear codes, to achieve all points in the achievable rate region of Slepian-Wolf [2] problem. The extension of these concepts to the construction of Euclidean-space codes is also studied and analyzed for the case of trellis and lattice codes. The performance of these symmetric methods for encoding with a fidelity criterion is shown to be the same as that of asymmetric encoding. Simulations are presented to corroborate these results.

JPEG-2000 is an emerging standard for still image compression. This paper provides a brief history of the JPEG-2000 standardization process, an overview of the standard, and some description of the capabilities provided by the standard. Part I of the JPEG-2000 standard specifies the minimum compliant decoder, while Part II describes optional, value-added extensions. Although the standard specifies only the decoder and bitstream syntax, in this paper we describe JPEG-2000 from the point of view of encoding. We take this approach, as we believe it is more amenable to a compact description more easily understood by most readers.

Subband and wavelet decompositions are powerful tools in image coding, because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter- and intra-band correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988 a growing body of research has examined the use of vector quantization for subband/wavelet transform coefficients. We present a survey of these methods. 1 Introduction Image compression maps an original image into a bit stream suitable for communication over or storage in a digital medium. The number of bits required to represent the coded image should b...

This paper investigates various classification techniques, applied to subband coding of images, as a way of exploiting the non-stationary nature of image subbands. The advantages of subband classification are characterized in a rate-distortion framework in terms of "classification gain" and overall "subband classification gain." Two algorithms, maximum classification gain and equal mean-normalized standard deviation classification, which allow unequal number of blocks in each class are presented. The dependence between the classification maps from different subbands is exploited either directly while encoding the classification maps or indirectly by constraining the classification maps. The trade-off between the classification gain and the amount of side information is explored. Coding results for a subband image coder based on classification are presented. The simulation results demonstrate the value of classification in subband coding. 1 Preface This paper is the result of a collabo...

ABSTRACT This paper presents an overview of wavelet-based image coding. We develop the basics of image coding with a discussion of vector quantization. We motivate the use of transform coding in practical settings,and describe the properties of various decorrelating transforms. We motivate the use of the wavelet transform in coding using rate-distortion considerations as well as approximation-theoretic considerations. Finally,we give an overview of current coders in the literature. 1