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