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

For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than ℓ1 penalty in enhancing the sparsity of solution. However, to date, the theory verifying that nonconvex penalties outperform (or are at least as good as) ℓ1 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 ℓ1 minimization.