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

TL;DR

This paper introduces SLS, a new greedy algorithm for sparse approximation that uses an L1-norm based selection rule, demonstrating superior performance in challenging sparse deconvolution tasks.

Contribution

The paper presents a novel greedy algorithm, SLS, which employs an L1-norm selection rule for improved sparse approximation over existing methods.

Findings

SLS outperforms popular greedy algorithms in simulations.

SLS surpasses Basis Pursuit Denoising in sparse deconvolution.

The method is effective with highly correlated dictionaries.

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.