Proximal alternating minimization method for adaptive TGV-based image restoration

This article presents an adaptive total generalized variation regularized strategy for image reconstruction. Unlike the traditional fixed weights schemes, our weights can be adaptively updated according to the latest computations. This helps to obtain more accurate numerical solutions and avoid the troublesome parameters selection. Subsequently, by artfully employing the Moreau decomposition and proximal algorithm, we develop a highly efficient proximal alternating minimization method to optimize the objective function in detail. The introduced technique has the capability of automatically estimating the regularization parameter and restoring the deteriorated image. Finally, several numerical simulations concertedly illustrate the competitive superiority of our proposed scheme for image restoration, especially in terms of suppressing staircase artifacts and maintaining edge details.