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A Greedy Sparse Approximation Algorithm Based On L1-Norm Selection Rules

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 L1-norm solutions. At each iteration, the regularization path of a least-squares criterion penalized by the L-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.https://hal.archives-ouvertes.fr/hal-01059414
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https://hal.archives-ouvertes.fr/hal-02563553
Contributor : Jérôme Idier <>
Submitted on : Monday, January 11, 2021 - 10:02:04 AM
Last modification on : Monday, February 22, 2021 - 12:34:08 PM

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Ramzi Ben Mhenni, Sébastien Bourguignon, Jérôme Idier. A Greedy Sparse Approximation Algorithm Based On L1-Norm Selection Rules. ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2020, Barcelona, Spain. pp.5390-5394, ⟨10.1109/ICASSP40776.2020.9054670⟩. ⟨hal-02563553⟩

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