Quantization of overcomplete expansions

Abstract

We present a method that represents a signal with respect to an overcomplete set of vectors which we call a dictionary. The use of overcomplete sets of vectors (redundant bases or frames) together with quantization is explored as an alternative to transform coding for signal compression. The goal is to retain the computational simplicity of transform coding while adding flexibility like adaptation to signal statistics. We show results using both fixed quantization in frames and greedy quantization using matching pursuit. An MSE slope of -6 dB/octave of frame redundancy is shown for a particular tight frame and is verified experimentally for another frame.