# Sparse recovery based on the generalized error function

arXiv: https://arxiv.org/abs/2105.13189 · HTML: https://mlsanity.com/paper/2105.13189/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 49 references that are in the map.
- First posted on arXiv 26 May 2021.

## Builds on (most cited first, 5 of 5)

- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [A Scale Invariant Approach for Sparse Signal Recovery](https://mlsanity.com/paper/1812.08852/) (2018)
- [DC approximation approaches for sparse optimization](https://mlsanity.com/paper/1407.0286/) (2014)
- [A Novel Regularization Based on the Error Function for Sparse Recovery](https://mlsanity.com/paper/2007.02784/) (2020)
- [A class of null space conditions for sparse recovery via nonconvex, non-separable minimizations](https://mlsanity.com/paper/1710.07348/) (2017)

## Built on by (most cited first, 1 of 1)

- [A Unified Framework for Constructing Nonconvex Regularizations](https://mlsanity.com/paper/2106.06123/) (2021)

## Abstract (arXiv)

In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established for both constrained and unconstrained models. The practical algorithms via both the iteratively reweighted ℓ1 and the difference of convex functions algorithms are presented. Numerical experiments are conducted to illustrate the improvement provided by the proposed approach in various scenarios. Its practical application in magnetic resonance imaging (MRI) reconstruction is studied as well.