Efficient quantization for overcomplete expansions in R/sup N/

The use of quantized redundant expansions is useful in applications where the cost of having oversampling in the representation is much lower than the use of a high-resolution quantization (e.g., oversampled A/D). Most work to date has assumed that simple uniform quantization was used on the redundant expansion and then has dealt with methods to improve the reconstruction. Instead, we consider the design of quantizers for overcomplete expansions. Our goal is to design quantizers such that simple reconstruction algorithms (e.g., linear) provide as good reconstructions as with more complex algorithms. We achieve this goal by designing quantizers with different step sizes for each coefficient of the expansion in such a way as to produce a quantizer with periodic structure.