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Optical Engineering

Adaptive time-frequency decompositions
Author(s): Geoffrey M. Davis; Stephane G. Mallat; Zhifeng Zhang
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Paper 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.

Paper Details

Date Published: 1 July 1994
PDF: 9 pages
Opt. Eng. 33(7) doi: 10.1117/12.173207
Published in: Optical Engineering Volume 33, Issue 7
Show Author Affiliations
Geoffrey M. Davis, New York Univ. (United States)
Stephane G. Mallat
Zhifeng Zhang, New York Univ. (United States)


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