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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.
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Contributor : Yann Traonmilin <>
Submitted on : Wednesday, June 20, 2018 - 10:26:56 AM
Last modification on : Saturday, July 11, 2020 - 3:14:58 AM
Long-term archiving on: : Monday, September 24, 2018 - 2:39:30 PM


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


Yann Traonmilin, Samuel Vaiter, Rémi Gribonval. Is the 1-norm the best convex sparse regularization?. iTWIST'18 - international Traveling Workshop on Interactions between low-complexity data models and Sensing Techniques, Nov 2018, Marseille, France. pp.1-11. ⟨hal-01819219⟩



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