This article concerns the improvement of digital image quality using mathematical tools such as nonlinear partial differential operators. In this paper, to perform smoothing on digital images, we propose to use the p(x)-Laplacian operator. Its smoothing power plays a main role in the restoration process. This enables us to dynamically process certain areas of an image. We used a mathematical model of image regularisation that is described by a nonlinear diffusion Equation (this diffusion is modelled by the p(x)-Laplacian operator). We implemented the continuous model in order to observe the steps of the regularisation process to understand the effects of the different parameters of the model on an image. This will enable parameters to be used and adapted in order to provide a proposed solution.