Sparse Recovery Based on the Generalized Error Function

Abstract

In this paper, we offer a new sparse recovery strategy based on the generalized error function. The introduced penalty function involves both the shape and the scale parameters, making it extremely flexible. For both constrained and unconstrained models, the theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established. The practical algorithms via both the iteratively reweighted $ℓ_1$ and the difference of convex functions algorithms are presented. Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances. Its practical application in magnetic resonance imaging (MRI) reconstruction is also investigated.