Adaptive timefrequency decompositions
Abstract
Computing the optimal expansion of a signal in a redundant dictionary of waveforms is an NPhard problem. We introduce a greedy algorithm, called a matching pursuit, which computes a suboptimal expansion. The dictionary waveforms that best match a signal's structures are chosen iteratively. An orthogonalized version of the matching pursuit is also developed. Matching pursuits are general procedures for computing adaptive signal representations. With a dictionary of Gabor functions, a matching pursuit defines an adaptive timefrequency transform. Matching pursuits are chaotic maps whose attractors define a generic noise with respect to the dictionary. We derive an algorithm that isolates the coherent structures of a signal and describe an application to pattern extraction from noisy signals.
 Publication:

Optical Engineering
 Pub Date:
 July 1994
 DOI:
 10.1117/12.173207
 Bibcode:
 1994OptEn..33.2183D