By combining fractional calculus and duality theory

a novel fractional-order primal-dual model

which is equivalent with the fractional ROF model

is proposed. We theoretically analyze its structural similarity with the saddle-point optimization model. So the algorithms for solving the saddle-point problem can be used for solving the model. The primal-dual algorithm based on resolvent for solving the saddle-point problem is used for solving the proposed model. The adaptive variable step size iterative optimization strategy is used

which can improve the optimizing efficiency

and remedy the step size limitation of the traditional numerical algorithms. In order to guarantee the convergence of the algorithm

the range of the parameter is given. The experiment results show that the proposed fractional-order primal-dual model is effective in avoiding the staircase effect and preserving texture and detail information

and the adoptive numerical algorithm has faster convergence speed. In this paper

we propose a fractional-order primal-dual denoising model

which can be solved by a primal-dual algorithm based on resolvent. The experiment results show that the proposed model can improve the image visual effect effectively

and the adoptive numerical algorithm has faster convergence speed.