Adaptive time-frequency decompositions

Geoffrey M. Davis; Stephane G. Mallat; Zhifeng Zhang

doi:10.1117/12.173207

1 July 1994 Adaptive time-frequency decompositions

Geoffrey M. Davis, Stephane G. Mallat, Zhifeng Zhang

Author Affiliations +

Optical Engineering, Vol. 33, Issue 7, (July 1994). https://doi.org/10.1117/12.173207

Abstract

Computing the optimal expansion of a signal in a redundant dictionary of waveforms is an NP-hard 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 time-frequency 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.

Citation Download Citation

Geoffrey M. Davis, Stephane G. Mallat, and Zhifeng Zhang "Adaptive time-frequency decompositions," Optical Engineering 33(7), (1 July 1994). https://doi.org/10.1117/12.173207

Published: 1 July 1994

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