Matching pursuit with stochastic selection

In this paper, we propose a Stochastic Selection strategy that accelerates the atom selection step of Matching Pursuit. This strategy consists of randomly selecting a subset of atoms and a subset of rows in the full dictionary at each step of the Matching Pursuit to obtain a sub-optimal but fast atom selection. We study the performance of the proposed algorithm in terms of approximation accuracy (decrease of the residual norm), of exact-sparse recovery and of audio declipping of real data. Numerical experiments show the relevance of the approach. The proposed Stochastic Selection strategy is presented with Matching Pursuit but applies to any pursuit algorithms provided that their selection step is based on the computation of correlations.