SLS (Single ${\ell }_1$ Selection): a new greedy algorithm with an ${\ell }_1$-norm selection rule

Abstract

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.

in Proceedings of iTWIST'20, Paper-ID: 24, Nantes, France, December, 2-4, 2020