SLS (Single $\ell_1$ Selection): a new greedy algorithm with an $\ell_1$-norm selection rule
This addresses sparse approximation problems in signal processing, but it is incremental as it builds on existing greedy methods with a modified selection rule.
The authors tackled sparse approximation by proposing SLS, a new greedy algorithm with an L1-norm selection rule, and showed it outperforms popular greedy algorithms and Basis Pursuit Denoising on difficult sparse deconvolution problems with highly correlated dictionaries when the solution is sparse.
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.