Is the 1-norm the best convex sparse regularization?

Abstract : The 1-norm is a good convex regularization for the recovery of sparse vectors from under-determined linear measurements. No other convex regularization seems to surpass its sparse recovery performance. How can this be explained? To answer this question, we define several notions of " best " (convex) regulariza-tion in the context of general low-dimensional recovery and show that indeed the 1-norm is an optimal convex sparse regularization within this framework.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01819219
Contributeur : Yann Traonmilin <>
Soumis le : mercredi 20 juin 2018 - 10:26:56
Dernière modification le : mercredi 18 juillet 2018 - 12:42:02

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optimal_reg_abstract_hal.pdf
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  • HAL Id : hal-01819219, version 1
  • ARXIV : 1806.08690

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Yann Traonmilin, Samuel Vaiter, Rémi Gribonval. Is the 1-norm the best convex sparse regularization?. 2018. 〈hal-01819219〉

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