  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.
