A New Stochastic Partial Differential Model for Image Restoration

Abstract

In this paper, we propose a stochastic partial differential equation model for the restoration of noisy images. This proposed model is based on the well-known Perona-Malik one, to which we add a stochastic process. The mathematical analysis of the proposed model is carried out within a well-defined framework, considering the specific conditions associated with an anisotropic diffusion. For the numerical approximation, we employ a stable finite difference scheme, ensuring its stability through Fourier analysis. The obtained numerical results demonstrate that our approach enhances images while preserving their important structure details, proving efficiency and competiveness compare to other approaches for image restoration.