An important task in image processing is the process of filling in missing parts of damaged images based on the information obtained from the surrounding areas. It is called inpainting. The goals of inpainting are numerous such as removing scratches in old photographic image, removing text and logos, restoration of damaged paintings. In this paper we present a nonlinear diffusion model for image inpainting based on a nonlinear partial differential equation as first proposed by Perona and Malik in [8]. In our previous work [3] the existence, uniqueness and regularity of the solution for the proposed mathematical model are established in an Hilbert space. The discretization of the partial differential equation of the proposed model is performed using finite elements method and finite differences method. For finite differences method our model is very simple to implement, fast, and produces nearly identical results to more complex, and usually slower, known methods. However for finite elements method we observe that it requires large computational cost, especially for high-resolution images. To avoid this slowing problem, domain decomposition algorithm has been proposed, aiming to split one large problem into many smaller problems. To illustrate the effective performance of our method, we present some experimental results on several images.

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Abstract. The image's restoration is an essential step in medical imaging. Several Filters are developped to remove noise, the most interesting are filters who permits to denoise the image preserving semantically important structures. One class of recent adaptive denoising methods is the nonlinear Partial Differential Equations who knows currently a significant success. This work deals with mathematical study for a proposed nonlinear evolution partial differential equation for image processing. The existence and the uniqueness of the solution are established. Using a finite differences method we experiment the validity of the proposed model and we illustrate the efficiently of the method using some medical images. The Signal to Noise Ration (SNR) number is used to estimate the quality of the restored images.

Abstract:The generation process of medical images is inevitably accompanied by a certain noise which degrades the quality of the image and assigns the final clinical diagnosis. Therefore, the denoising step plays an important role in the treatment of medical images in order to prepare the steps of diagnosis and therapy. In this paper, we propose a nonlinear diffusion model for denoising of large size images. The numerical approach to this problem is based on an algorithm combining the methods of finite element and of domain decomposition. Numerical simulations show that the proposed algorithm is a useful alternative for the treatment of degraded images large size.

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