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arXiv · 1710.07348

A class of null space conditions for sparse recovery via nonconvex, non-separable minimizations

Hoang Tran·Clayton Webster
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Abstract

For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than $\ell_1$ penalty in enhancing the sparsity of solution. However, to date, the theory verifying that nonconvex penalties outperform (or are at least as good as) $\ell_1$ minimization in exact, uniform recovery has mostly been limited to separable cases. In this paper, we establish general recovery guarantees through null space conditions for nonconvex, non-separable regularizations, which are slightly less demanding than the standard null space property for $\ell_1$ minimization.

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Hoang Tran, Clayton Webster. 2017-10-19. A class of null space conditions for sparse recovery via nonconvex, non-separable minimizations. https://arxiv.org/abs/1710.07348

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