Sparse approximations with a high resolution greedy algorithm

Signal decomposition with an overcomplete dictionary is nonunique. Computation of the best approximation is known to be NP-hard problem. The matching pursuit (MP) algorithm is a popular iterative greedy algorithm that finds a sub-optimal approximation, by picking at each iteration the vector that best correlates with the present residual. Choosing approximation vectors by optimizing a correlation inner product can produce a loss of time and frequency resolution. We propose a modified MP, based on a post processing step applied on the resulting MP approximation, using the backward greedy algorithm, to achieve higher resolution than the original MP.