Non-convex fractional-order TV model for image inpainting

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, which is designed to overcome the limitations of classical total variation and higher-order derivative methods that often result in the undesirable staircase effect and blurred contours. This innovative technique effectively mitigates these issues, significantly improving restoration quality. Numerically, to tackle the constructed optimization problem, we design a practical primal–dual algorithm that integrates with the iteratively reweighted \(\ell _1\) ${\ell }_1$ algorithm. Extensive simulation experiments demonstrate that our method achieves the remarkable improvements of approximately 5% in PSNR, and 3% in both SSIM and FSIM compared to other approaches, conclusively showing its capability to deliver visually realistic inpainting results with superior quantitative metrics.