Sparse and structured decompositions of signals with the molecular matching pursuit
- 21 August 2006
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Audio, Speech, and Language Processing
- Vol. 14 (5), 1808-1816
- https://doi.org/10.1109/tsa.2005.858540
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 signalsKeywords
This publication has 15 references indexed in Scilit:
- Audio source separation with a single sensorIEEE Transactions on Audio, Speech, and Language Processing, 2005
- MDCT Analysis of Sinusoids: Exact Results and Applications to Coding Artifacts ReductionIEEE Transactions on Speech and Audio Processing, 2004
- Harmonic decomposition of audio signals with matching pursuitIEEE Transactions on Signal Processing, 2003
- Orthogonal matching pursuit: recursive function approximation with applications to wavelet decompositionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Matching pursuit with damped sinusoidsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Fast matching pursuit with a multiscale dictionary of Gaussian chirpsIEEE Transactions on Signal Processing, 2001
- Image Feature Extraction and Denoising by Sparse CodingPattern Analysis and Applications, 1999
- Sinusoidal modeling using frame-based perceptually weighted matching pursuitsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1999
- Embedded image coding using zerotrees of wavelet coefficientsIEEE Transactions on Signal Processing, 1993
- Matching pursuits with time-frequency dictionariesIEEE Transactions on Signal Processing, 1993