Gauss Mixture Quantization for Image Compression and Segmentation

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The research is concerned with techniques from statistical signal processing and information theory as they apply to communication systems with multiple goals. Such systems arise in multimedia communications networks like the Internet. The decomposition of data streams into different types is critical to finding information desired by a user among vast available sources, and it can also provide methods for displaying, rendering, printing, or playing the received signal that take advantage of its particular structure. Signal processing and coding theory have provided powerful mathematical models of information sources and algorithms by which these sources can be communicated and processed. Typically systems are designed as a collection of separate, unrelated, components. This can result in much less than optimal overall performance. Furthermore, it can hamper theoretical understanding of the fundamental limits on achievable performance.We treat the simultaneous design of mathematical models that account at once for information sources, data compression, and signal processing and apply to extracting information from the received data. Our emphasis is on image communication and processing. Because, the techniques draw heavily from demonstrably successful methods in speech coding and recognition they are natural for both signal types, individually or together.The research involves a unified approach to data compression, statistical classification and regression, and density estimation. It is based on a novel combination of vector quantization, Gauss mixture models, measures of minimum discrimination information (relative entropy), and universal coding. Vector quantization provides both a theoretical framework and a method for implementation. Gauss mixture models are a flexible class by which to describe information sources. They can be fit to real data by clustering with respect to a minimum discrimination information measure of distortion. A primary objective is the development and application of conditional versions of rate-distortion extremal properties of Gaussian models in order to design robust algorithms for compression, classification, modeling, and combinations thereof. There are many open questions about relations among modeling, compression, and classification/regression. Our goal is to provide answers to as many of them as possible and in so doing to contribute to understanding the interplay of modeling, signal processing, and coding. We describe optimized and implementable robust codes for compression and classification for a variety of information sources, especially for multimodal imagery. Part of our efforts are devoted to purely mathematical aspects of tree-structured regression, which is related to martingale theory and to the differentiation of integrals.