Performance analysis from rate distortion theory of wavelet domain vector quantization encoding
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Vector quantization can be addressed from two major optimization criteria: efficient codebook generation by clustering algorithms with global solutions and optimal encoding with die codebook. Both have been under intense study in recent years. This dissertation gives an in-depth analysis of three well-known clustering algorithms from three different theoretical frameworks in their application to vector quantization. Their efficiencies for codebook training are analyzed and compared with lower bounds from rate-distortion theory. Such an analytical study provides guidelines on the selection of a proper clustering algorithm for vector quantization codebook training. With the codebook generated from a chosen clustering algorithm, a novel hybrid quantization scheme to preserve detail information of an image is also proposed in this dissertation. Motivated by the efficiency of the zerotree scalar coding of wavelet transform coefficients, such as the embedded zerotree wavelet (EZW) and set partitioning in hierarchical trees (SPIHT) algorithms, several attempts have been made recently to adopt similar methodologies to discard insignificant coefficients (or zerotrees) prior to employing traditional vector partitioning. This latter approach to combine vector quantization with zerotree elimination, however, fails to retain fine details, e.g., edge information, with a reasonable codebook size. In the proposed scheme, edge information can be preserved without excessive increase in the codebook size by creating a universal codebook with a combination of vector quantization and residual scalar coding of a few large magnitude wavelet coefficients. The efficiency of this hybrid multiscale vector quantizer (HMVQ) for medical images is demonstrated by encoding MR images and achieving at least 2 dB PSNR improvement over SPIHT at low bit rates. Preservation of fine details even at low bit rates is a desirable characteristic of HMVQ, particularly when medical image coding is concerned. The performance of HMVQ by using a preliminary universal codebook in decoding images with less distortion than the SPIHT decoder at low bit rates is also presented.