Sparse and structured decompositions of signals with the molecular matching pursuit

  • Authors:
  • L. Daudet

  • Affiliations:
  • Lab. d'Acoustique Musicale, Univ. Pierre et Marie Curie, Paris

  • Venue:
  • IEEE Transactions on Audio, Speech, and Language Processing
  • Year:
  • 2006

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Abstract

This paper describes the Molecular Matching Pursuit (MMP), an extension of the popular Matching Pursuit (MP) algorithm for the decomposition of signals. The MMP is a practical solution which introduces the notion of structures within the framework of sparse overcomplete representations; these structures are based on the local dependency of significant time-frequency or time-scale atoms. We show that this algorithm is well adapted to the representation of real signals such as percussive audio signals. This is at the cost of a slight sub-optimality in terms of the rate of convergence for the approximation error, but the benefits are numerous, most notably a significant reduction in the computational cost, which facilitates the processing of long signals. Results show that this algorithm is very promising for high-quality adaptive coding of audio signals