Non-convex fractional-order TV model for image inpainting

Abstract This paper aims to address the challenge of effectively processing missing or corrupted image areas using the known image information. In this study, we consider a novel non-convex and non-smooth variational model tailored for image inpainting. Our scheme introduces the non-convex potential function into the fractional order total variation regularization. This innovative technique effectively mitigates blurred contours and alleviates the undesirable staircase effect, significantly improving restoration quality. Numerically, to tackle the generated optimization problem, we design a practical primal-dual algorithm that integrates with the iteratively reweighted 1 algorithm. Extensive simulation experiments, comparing our novel model with other approaches, conclusively demonstrate its capability to achieve the visually realistic inpainting while yielding the highest quantitative results.