A denoising model adapted for impulse and Gaussian noises using a constrained-PDE

Abstract

In denoising problems, it is always hard to deal with a mixture of two noise densities. In this paper, we introduce a nonlinear constrained-PDE based on the fractional order tensor diffusion to approximate the clean image and also the impulse component in a mixture of Gaussian and impulse noise. Our model offers an ideal compromise between the edge preservation, staircasing creation and the loss of image contrasts. The proposed constrained-PDE is formulated using a variational model that features a L1 data discrepancy encoding the impulse noise and an L2 term of the clean image, which is a solution of a high-order PDE. Then, a rigorous analysis of the existence of the solution to the proposed model is checked in a suitable functional framework. In addition, to solve the constrained-PDE, we consider an extension of the primal-dual algorithm to nonlinear operators with an accelerate Bregman iteration. Numerical experiments show that the proposed model produces pleasant results in terms of restoration quality and solution efficiency compared to some competitive regularizations.