Is the 1-norm the best convex sparse regularization?
Information Theory
2018-06-25 v1 math.IT
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.
Cite
@article{arxiv.1806.08690,
title = {Is the 1-norm the best convex sparse regularization?},
author = {Yann Traonmilin and Samuel Vaiter and Rémi Gribonval},
journal= {arXiv preprint arXiv:1806.08690},
year = {2018}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1803.00773