Universal multiresolution source codes

A multiresolution source code is a single code giving an embedded source description that can be read at a variety of rates and thereby yields reproductions at a variety of resolutions. The resolution of a source reproduction here refers to the accuracy with which it approximates the original source. Thus, a reproduction with low distortion is a “high-resolution” reproduction while a reproduction with high distortion is a “low-resolution” reproduction. This paper treats the generalization of universal lossy source coding from single-resolution source codes to multiresolution source codes. Results described in this work include new definitions for weakly minimax universal, strongly minimax universal, and weighted universal sequences of fixed- and variable-rate multiresolution source codes that extend the corresponding notions from lossless coding and (single-resolution) quantization to multiresolution quantizers. A variety of universal multiresolution source coding results follow, including necessary and sufficient conditions for the existence of universal multiresolution codes, rate of convergence bounds for universal multiresolution coding performance to the theoretical bound, and a new multiresolution approach to two-stage universal source coding

A Study of trellis coded quantization for image compression

Trellis coded quantization has recently evolved as a powerful quantization technique in the world of lossy image compression. The aim of this thesis is to investigate the potential of trellis coded quantization in conjunction with two of the most popular image transforms today; the discrete cosine transform and the discrete wavelet trans form. Trellis coded quantization is compared with traditional scalar quantization. The 4-state and the 8-state trellis coded quantizers are compared in an attempt to come up with a quantifiable difference in their performances. The use of pdf-optimized quantizers for trellis coded quantization is also studied. Results for the simulations performed on two gray-scale images at an uncoded bit rate of 0.48 bits/pixel are presented by way of reconstructed images and the respective peak signal-to-noise ratios. It is evident from the results obtained that trellis coded quantization outperforms scalar quantization in both the discrete cosine transform and the discrete wavelet transform domains. The reconstructed images suggest that there does not seem to be any considerable gain in going from a 4-state to a 8-state trellis coded quantizer. Results also suggest that considerable gain can be had by employing pdf-optimized quantizers for trellis coded quantization instead of uniform quantizers

Rate-cost tradeoffs in control

Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state

Generalizations of permutation source codes

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 87-90).Permutation source codes are a class of structured vector quantizers with a computationally- simple encoding procedure. In this thesis, we provide two extensions that preserve the computational simplicity but yield improved operational rate-distortion performance. In the first approach, the new class of vector quantizers has a codebook comprising several permutation codes as subcodes. Methods for designing good code parameters are given. One method depends on optimizing the rate allocation in a shape-gain vector quantizer with gain-dependent wrapped spherical shape codebook. In the second approach, we introduce frame permutation quantization (FPQ), a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of possible quantization rates and a higher maximum rate. Various representations for the partitions induced by FPQ are presented and reconstruction algorithms based on linear programming and quadratic programming are derived. Reconstruction using the canonical dual frame is also studied, and several results relate properties of the analysis frame to whether linear reconstruction techniques provide consistent reconstructions. Simulations for uniform and Gaussian sources show performance improvements over entropy-constrained scalar quantization for certain combinations of vector dimension and coding rate.by Ha Quy Nguyen.S.M