Optimal modeling for complex system design

The article begins with a brief introduction to the theory describing optimal data compression systems and their performance. A brief outline is then given of a representative algorithm that employs these lessons for optimal data compression system design. The implications of rate-distortion theory for practical data compression system design is then described, followed by a description of the tensions between theoretical optimality and system practicality and a discussion of common tools used in current algorithms to resolve these tensions. Next, the generalization of rate-distortion principles to the design of optimal collections of models is presented. The discussion focuses initially on data compression systems, but later widens to describe how rate-distortion theory principles generalize to model design for a wide variety of modeling applications. The article ends with a discussion of the performance benefits to be achieved using the multiple-model design algorithms

Weighted universal image compression

We describe a general coding strategy leading to a family of universal image compression systems designed to give good performance in applications where the statistics of the source to be compressed are not available at design time or vary over time or space. The basic approach considered uses a two-stage structure in which the single source code of traditional image compression systems is replaced with a family of codes designed to cover a large class of possible sources. To illustrate this approach, we consider the optimal design and use of two-stage codes containing collections of vector quantizers (weighted universal vector quantization), bit allocations for JPEG-style coding (weighted universal bit allocation), and transform codes (weighted universal transform coding). Further, we demonstrate the benefits to be gained from the inclusion of perceptual distortion measures and optimal parsing. The strategy yields two-stage codes that significantly outperform their single-stage predecessors. On a sequence of medical images, weighted universal vector quantization outperforms entropy coded vector quantization by over 9 dB. On the same data sequence, weighted universal bit allocation outperforms a JPEG-style code by over 2.5 dB. On a collection of mixed test and image data, weighted universal transform coding outperforms a single, data-optimized transform code (which gives performance almost identical to that of JPEG) by over 6 dB

Vector quantization

During the past ten years Vector Quantization (VQ) has developed from a theoretical possibility promised by Shannon's source coding theorems into a powerful and competitive technique for speech and image coding and compression at medium to low bit rates. In this survey, the basic ideas behind the design of vector quantizers are sketched and some comments made on the state-of-the-art and current research efforts

Low bit rate speech coding methods and a new interframe differential coding scheme for line spectrum pairs

Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 1992.Thesis (Master's) -- Bilkent University, 1992.Includes bibliographical references leaves 30-32.Low bit rate speech coding techniques and a new coding scheme for vocal tract parameters are presented. Linear prediction based voice coding techniques (linear predictive coding and code excited linear predictive coding) are examined and implemented. A new interframe differential coding scheme for line spectrum pairs is developed. The new scheme reduces the spectral distortion of the linear predictive filter while maintaining a high compression ratio.Erzin, EnginM.S

Suboptimality of the Karhunen-Loève transform for transform coding

We examine the performance of the Karhunen-Loeve transform (KLT) for transform coding applications. The KLT has long been viewed as the best available block transform for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. This paper treats fixed-rate and variable-rate transform codes of non-Gaussian sources. The fixed-rate approach uses an optimal fixed-rate scalar quantizer to describe the transform coefficients; the variable-rate approach uses a uniform scalar quantizer followed by an optimal entropy code, and each quantized component is encoded separately. Earlier work shows that for the variable-rate case there exist sources on which the KLT is not unique and the optimal quantization and coding stage matched to a "worst" KLT yields performance as much as 1.5 dB worse than the optimal quantization and coding stage matched to a "best" KLT. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for using a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding

A vector quantization approach to universal noiseless coding and quantization

A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n -1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n-1) when the universe of sources is countable, and as O(n-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions

Efficient compression of motion compensated residuals

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An optimal design procedure for intraband vector quantized subband coding

Journal ArticleAbstTact- Subband coding with vector quantization is addressed in this paper. Forming the data vectors from both between and within the subbands is considered. The former of these two schemes is referred to as interband coding and the latter as intraband coding. Interband coder design is relatively straightforward since the design of the single codebook involved follows readily from a representative set of interband data vectors. Intraband coder design is more complicated since it entails the selection of a vector dimension and a bit-rate for each subband. The main contribution of this work is an optimal methodology for intraband subband vector quantizer design. The problem formulation includes constraints on the bit-rate and the encoding complexity and is solved with nonlinear programming methods. Subband vector quantization image coding in conjunction with a human visual system model is thoroughly investigated. Results of a large number of experiments indicate that the optimal intraband coder yields superior results from quantitative as well as subjective points of view than the interband coder for comparable bit-rates. This improvement becomes more pronounced as the computational complexity of the intraband encoder is allowed to increase