A denoising model based on the fractional Beltrami regularization and its numerical solution

In image processing, the regularization term is always hard to choose. In this paper, we introduce a model based on the fractional derivative, which is derived from the classical Beltrami model. The proposed regularization term offers an ideal compromise between feature preservation, avoidance of staircasing and the loss of image contrasts. This model can outperform the high order regularization models and also the total fractional-order variation model. Also, we rigorously analyse the theoretical properties of the fractional derivative and show the existence and uniqueness of the proposed minimization problem in a suitable functional framework. In addition, to solve the variational problem, we consider the primal-dual projected gradient algorithm. Numerical experiments show that the proposed model produces competitive results compared to some classical regularizations, especially, it avoids the staircase effect and preserves edges and features of the image while reducing noise.