Sparse Recovery Based on the Generalized Error Function (Journal of Computational Mathematics, 2024)
In this paper, we offer a new sparse recovery strategy based on the generalized errorfunction. 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 sectionproperty and the restricted invertibility factor are established. The practical algorithmsvia both the iteratively reweighted $ℓ_1$ and the difference of convex functions algorithmsare presented. Numerical experiments are carried out to demonstrate the benefits of thesuggested approach in a variety of circumstances. Its practical application in magneticresonance imaging (MRI) reconstruction is also investigated.
Keywords: Sparse recovery; Generalized error function; Nonconvex regularization; Iterative reweighted L1; Difference of convex functions algorithms.