Greedy methods for simultaneous sparse approximation

This paper extends greedy methods to simultaneous sparse approximation. This problem consists in finding good estimation of several input signals at once, using different linear combinations of a few elementary signals, drawn from a fixed collection. The sparse algorithms for which simultaneous versions are proposed are namely CoSaMP, OLS and SBR. These approaches are compared to Tropp´s S-OMP algorithm using simulation signals. We show that in the case of signals exhibiting correlated components, the simultaneous versions of SBR and CoSaMP perform better than S-OMP and S-OLS.