Non-Convex Total Generalized Variation with Spatially Adaptive Regularization Parameters for Edge-Preserving Image Restoration

Abstract

Restoration of images from noisy and blurred data is an ill-posed inverse problem which has gained considerable attention in recent years. To handle the ill-posed nature of this problem, many convex variational methods have been proposed to enhance the image quality. Motivated by the success of non-convex minimization, we formulate image restoration problem in this paper as a least-squares optimization problem constrained by a non-convex second-order regularizer. The proposed non-convex variational method is able to effectively reduce both blurring and noise effects while preserving the important structural information of images. To further improve image quality, a local expected variance estimate-based scheme is introduced to adaptively calculate the regularization parameters. An iteratively reweighted algorithm based on alternating direction method of multipliers is developed to solve the resulting non-convex optimization problem. Extensive experiments have been conducted to compare the proposed method with several current state-of-the-art image restoration methods. Numerical results have illustrated the superior performance of our proposed method under different image degradation conditions.