SLS (Single $\ell_1$ Selection): a new greedy algorithm with an $\ell_1$-norm selection rule
Optimization and Control
2021-02-12 v1 Machine Learning
Computation
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.
Cite
@article{arxiv.2102.06058,
title = {SLS (Single $\ell_1$ Selection): a new greedy algorithm with an $\ell_1$-norm selection rule},
author = {Ramzi Ben Mhenni and Sébastien Bourguignon and Jérôme Idier},
journal= {arXiv preprint arXiv:2102.06058},
year = {2021}
}
Comments
in Proceedings of iTWIST'20, Paper-ID: 24, Nantes, France, December, 2-4, 2020