Sparse Recovery Based on the Generalized Error Function

In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both shape and scale parameters, making it very flexible. theoretical analysis results in terms of null space property, spherical section property restricted invertibility factor are established for constrained unconstrained models. practical algorithms via iteratively reweighted $\ell_1$ difference convex functions presented. Numerical experiments conducted to illustrate improvement provided by proposed approach various scenarios. Its application magnetic resonance imaging (MRI) reconstruction is studied as well.