In this paper, we propose a variational model incorporating an \(L^{1}\) -norm regularization term using weighted variable-order Riesz fractional derivatives (WVO-RFDs) to remove additive noise in images. The variational problem is discretized by composite Trapezoidal rule as well as an approximate scheme for the left and right variable-order Riemann–Liouville fractional derivatives and finally deduce a minimization problem in a finite-dimensional space. With the help of proximity operators, the optimization problem is solved by a proximity algorithm. Compared with other image denoising models, the experimental results given by the proposed method in this paper show the efficient performance while using WVO-RFDs in image denoising.
