Wavelet vector quantization with matching pursuit

To compute the optimal expansion of signals in redundant dictionary of waveforms is an NP complete problem. We introduce a greedy-algorithm, called matching pursuit, that performs a sub-optimal expansion. This algorithm can be interpreted as a shape-gain multistage vector quantization. The waveforms are chosen iteratively in order to best match the signal structures. Matching pursuits are general procedures used to compute adaptive signal representations. Applications to speech and image processing with dictionaries of Gabor functions are shown, in particular for the noise removal.