Mixed Noise Removal Framework Using a Nonlinear Fourth-Order PDE-Based Model

Abstract

A novel partial differential equation (PDE)—based mixed image noise removal technique is proposed in this article. The considered approach filters successfully the images corrupted by combined Poisson–Gaussian noise by using a nonlinear fourth-order PDE-based denoising model that is proposed and carefully investigated here. Thus, a rigorous mathematical treatment of the validity of this model is performed, the existence of a weak solution of it being demonstrated. Then, the nonlinear PDE model is solved numerically by constructing a stable and fast-converging finite difference-based approximation scheme that is consistent to it. Mixed noise reduction experiments illustrating the effectiveness of the proposed approach are also discussed.