A non-convex PDE-constrained denoising model for impulse and Gaussian noise mixture reduction

Abstract

<p style='text-indent:20px;'>This paper introduces a novel optimization procedure to reduce a mixture of Gaussian and impulse noise from images. This framework is based on a non-convex PDE-constrained with two diffusion operators: a local weickert and a fractional-order ones. The non-convex norm is applied to remove the impulse component, while the local and fractional operators are introduced to preserve image texture and edges. In the first part, we study the theoretical properties of the proposed PDE-constrained, and we show some well-posedness results. In a second part, after having demonstrated how to numerically find a minimizer, a proximal linearized algorithm combined with a Primal-Dual approach is introduced with local convergence results. Finally, we show extensive denoising experiments on various images and noise intensities which confirms the validity of the non-convex PDE-constrained, its analysis and also the proposed optimization procedure.</p>