Adaptive Time-Frequency Approximations with Matching Pursuits

Abstract

Computing the optimal expansion of a signal in a redundant dictionary of waveforms is an NP-complete problem. We introduce a greedy algorithm called a matching pursuit which computes a sub optimal expansion. The dictionary waveforms which best match a signals 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. We derive a signal energy distribution in the time-frequency plane which does not contain interference terms, unlike the Wigner and Cohen class distributions. A matching pursuit is a chaotic map whose asymptotic properties are studied. We describe an algorithm which isolates the coherent structures of a signal and show an application to pattern extraction from noisy signals.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1994
Accession Number
AD1020214

Entities

People

  • Geoffrey Davis
  • Stephane Mallat
  • Zhifeng Zhang

Organizations

  • New York University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Dictionaries
  • Extraction
  • Frequency
  • Frequency Shift
  • Waveforms

Fields of Study

  • Engineering

Readers

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  • Image Processing and Computer Vision.