Quantization Design for Structured Overcomplete Expansions

The study of quantized overcomplete (redundant) expansions is relevant to several important applications such as oversampled A/D conversion of band-limited signals, multiple description quantization, joint source-channel coding and contentbased retrieval for image databases. The problem of quantization of overcomplete expansions is not as well understood as that of quantization of more traditional critically sampled (non-redundant) expansions. As an example, in the latter case, one can minimize the overall distortion by minimizing the distortion independently in each of the expansion coefficients. This is not true for an overcomplete expansion. Previous research work to date has assumed only simple quantization schemes and has focused on finding improved reconstruction algorithms. In our work, we study different issues related to overcomplete expansions, focusing on designing efficient quantization techniques for this type of decompositions. More specifically, the following topics are studied:

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