Sparse and structured decompositions of signals with the molecular matching pursuit

algorithm for the decomposition of signals. The MMP is a prac-tical solution which introduces the notion of structures within the framework of sparse overcomplete representations; these struc-tures are based on the local dependency of significant time-fre-quency 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 ben-efits are numerous, most notably a significant reduction in the com-putational cost, which facilitates the processing of long signals. Re-sults show that this algorithm is very promising for high-quality adaptive coding of audio signals. Index Terms—Matching pursuit, overcomplete representations, parametric audio coding, time-frequency transforms. I