Image Denoising Based On Graph Regularization Diffusion

Image denoising is the classic issue of digital image processing. Anisotropic diffusion model is one of the typical PDE based image denoising methods, which is also called P-M model. Its idea is to control the smoothness of diffusion using image gradient which represents edges, so this method is a non-linear adaptive denoising method. P-M diffusion process is ill-posed, so it needs to be translated into a well-posed problem via regularization before solved. When defining images on a continuous space, it's difficult for the implementation of algorithms to achieve the requirements of being fast, accurate and numerically stable. After introducing graph theory, images can be represented by any graph topology, and the weights of graph edges make the diffusion based denoising somewhat adaptive. During the process of image denoising based on regularization, it's contradictory to preserve edges and clear noise at the same time. Global regularization methods use a single regularization parameter operator for the whole image, and it has a same punishment to edges and noise, so it's hard to resolve the contradiction. Although, the introduction of graph theory make the denoising method has some adaptive properties, the method is still limited because of the global regularization parameter.Compared with global regularization, adaptive regularization methods use different parameters and operators in different regions, so they can operate the edges and noise differentially. Aiming at the disadvantage of global regularization, combining with graph theory, this thesis proposes an image denoising model using graph based adaptive regularization. Edge regions are decided via the gradients on the graph and regularization parameters are adaptively set. and set regularization parameters adaptively. According to different parameters, different penalizes are applied to the edge region and non-edge region to get different effects. In this way the contradiction between preserving edges and clearing noise is resolved.By using the proposed model and some other denoising models to clear the Gaussian noise in images and then comparing them, the result shows that, at subject performance and objective performance, at preserving edges and clearing noise, the proposed model is better than graph based global regularization methods and other diffusion based denoising methods. Furthermore, the algorithm can converge quickly to a good denoising result. From the foregoing, The proposed method is an effective image denoising method.