Sparse and structured decompositions of signals with the Molecular Matching Pursuit

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.