Adaptive time-frequency decompositions with matching pursuit

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

doi:10.1117/12.170041

15 March 1994 Adaptive time-frequency decompositions with matching pursuit

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

Proceedings Volume 2242, Wavelet Applications; (1994) https://doi.org/10.1117/12.170041
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

Abstract

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 suboptimal expansion. The waveforms are chosen iteratively in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions, a matching pursuit defines an adaptive time-frequency transform. We derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit is a chaotic map, whose attractor defines a generic noise with respect to the dictionary. We derive an algorithm that isolates the coherent structures of a signal and an application to pattern extraction from noisy signals is described.

Citation Download Citation

Geoffrey M. Davis, Stephane G. Mallat, and Zhifeng Zhang "Adaptive time-frequency decompositions with matching pursuit", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170041

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