# SLS (Single ℓ1 Selection): a new greedy algorithm with an ℓ1-norm selection rule

arXiv: https://arxiv.org/abs/2102.06058 · HTML: https://mlsanity.com/paper/2102.06058/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
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- First posted on arXiv 11 Feb 2021.

## Abstract (arXiv)

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.