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In this paper, we propose a new greedy algorithm for sparse approximation,called SLS for Single L_1 Selection. SLS essentially consists of a greedyforward strategy, where the selection rule of a new component at each iterationis based on solving a least-squares optimization problem, penalized by the L_1norm of the remaining variables. Then, the component with maximum amplitude isselected. Simulation results on difficult sparse deconvolution problemsinvolving a highly correlated dictionary reveal the efficiency of the method,which outperforms popular greedy algorithms and Basis Pursuit Denoising whenthe solution is sparse.

SLS (Single $\ell_1$ Selection): a new greedy algorithm with an $\ell_1$-norm selection rule