Fractional‐Order Total Variation Image Restoration Based on Primal‐Dual Algorithm

This paper proposes a fractional‐order total variation image denoising algorithm based on the primal‐dual method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill‐posed inverse, convergence rate, and blocky effect. The fractional‐order total variation model is introduced by generalizing the first‐order model, and the corresponding saddle‐point and dual formulation are constructed in theory. In order to guarantee O(1/N2) convergence rate, the primal‐dual algorithm was used to solve the constructed saddle‐point problem, and the final numerical procedure is given for image denoising. Finally, the experimental results demonstrate that the proposed methodology avoids the blocky effect, achieves state‐of‐the‐art performance, and guarantees O(1/N2) convergence rate.