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

https://doi.org/10.1016/j.rinam.2019.100011Get rights and content
Under a Creative Commons license
open access

Abstract

For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than 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) 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 1 minimization.

Keywords

Nonconvex optimization
Null space property
Sparse recovery
Majorization theory

AMS subject classifications

94A12
94A15
90C26

Cited by (0)