A Greedy Sparse Approximation Algorithm Based On L1-Norm Selection Rules
Ramzi Ben Mhenni, Sébastien Bourguignon, Jérôme Idier
Abstract
We propose a new greedy sparse approximation algorithm, called SLS for Single L1 Selection, that addresses a least squares optimization problem under a cardinality constraint. The specificity and increased efficiency of SLS originate from the atom selection step, based on exploiting ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm solutions. At each iteration, the regularization path of a least-squares criterion penalized by the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm of the remaining variables is built. Then, the selected atom is chosen according to a scoring function defined over the solution path. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms when the solution is sparse.
BibTeX
@inproceedings{icassp2020_agreedysparseapp,
title = {A Greedy Sparse Approximation Algorithm Based On L1-Norm Selection Rules},
author = {Ramzi Ben Mhenni and Sébastien Bourguignon and Jérôme Idier},
booktitle = {ICASSP 2020},
year = {2020}
}