Source coding of composite sources with segmental fidelity measures.

Abstract

This dissertation develops vector quantization theory for composite source models and segmental fidelity measures. A composite source consists of a collection of modes and a switch. At a given time the switch chooses a mode, whose output becomes the composite source output, until it chooses another. Unlike homogeneous r and om processes, composite sources can easily capture the multimodality of physical sources, such as speech and raster scanned images. Segmental fidelity measures apply different weightings to the fidelity achieved on different modes, accounting for the fact that a context sensitive user's perception of distortion is different on different modes. This dissertation presents results on designing and analyzing the performance of optimum vector quantizers in three different coding scenarios involving composite sources and three segmental fidelity measures: namely, vector quantization with no mode classifier; vector quantization with a perfect classifier; and vector quantization with an imperfect mode classifier. Specifically, (1) the optimum quantization regions and vectors are found to be nearest neighbor regions and generalized centroids, respectively; (2) algorithms for designing optimum vector quantizers are developed, exploiting the above optimality conditions; (3) Bennett and Zador-like asymptotic formulas for the performance and optimum performance, respectively, are found for large rate; (4) relations between the optimum performance for a composite source and those for its modes are found; and (5) preliminary tests on speech suggest that this approach does indeed design better quantizers than traditional approaches. Also presented is a new development of high resolution quantization theory for the traditional rth power distortion measure. This new approach is more rigorous and direct than previous work. The major contributions of this dissertation are: (1) it provides a more general framework for source coding theory, in that composite sources include homogeneous r and om processes, and segmental fidelity measures include, as well as the mean squared error distortion measure, measures devised to meet the specific tastes and needs of various users; (2) it shows that a theory of waveform source coding based on composite sources and segmental fidelity measures is both tractable and useful; and (3) it develops a rigorous and direct high resolution quantization theory.