A Novel Fractional-Order Non-Convex TVα,p Model in Image Deblurring

In this paper, we propose a non-convex model with fractional-order applied to image deblurring problems. In the new model, fractional-order gradients have been introduced to preserve detailed features, and a source term with a blurry kernel is used for deblurring. This aspect of the model ensures that it can handle various blurring scenarios. Additionally, we devise an algorithm that maintains the non-expansiveness of the support set for image gradients, serving as a critical component in our approach to address image deblurring issues. After approximate linearization, the algorithm can be easily implemented. Some standard image processing techniques similar to fast Fourier transform can be utilized. Global convergence has likewise been confirmed and established. Moreover, we have also demonstrated that the proposed deblurring algorithm exhibits edge preservation properties. Compared with several existing classic models, the proposed method maintains a good balance between detail preservation, edge preservation, and deblurring. In addition, compared with several classic methods, the proposed method improved PSNR and SSIM by 0.9733 and 0.0111, respectively.