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

arXiv: https://arxiv.org/abs/1710.07348 · HTML: https://mlsanity.com/paper/1710.07348/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2017.

## Built on by (most cited first, 4 of 4)

- [On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples](https://mlsanity.com/paper/2203.13908/) (2022)
- [Sparse recovery based on the generalized error function](https://mlsanity.com/paper/2105.13189/) (2021)
- [Learning k-Level Structured Sparse Neural Networks Using Group Envelope Regularization](https://mlsanity.com/paper/2212.12921/) (2022)
- [Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm](https://mlsanity.com/paper/2606.19046/) (2026)

## Abstract (arXiv)

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.