Study On Image Restoration Based On Partial Differential Equation

Image restoration is one of the hot topics in computer graphics and computer vision, and has been widely applied in natural sciences and engineering technology. In the natural conditions, the images may be damaged to different degree during the process of transmission and storage, and therefore, part of the image information may be missing. The missing information can certainly affect not only the visual effect of the damaged images, but also the image processing on such images. Thus, it is particularly important to investigate the approaches of image restoration.In this dissertation, image restoration algorithms based on partial differential equation are introduced firstly, and a new image restoration algorithm is proposed. As one of the most widely used image restoration algorithm, the TV (Total Variation) model is an anisotropic diffusion method, which can well protect the image edge information. However, in the flat areas of the image, where the image gradient is low, the TV anisotropic diffusion model can easily generate ladder effect, and result in blurred and false edge. While the P-Laplace algorithm, as an isotropic diffusion method, can obtain satisfying restoration results in the flat areas of the damaged images. However, the P-Laplace algorithm can’t meet the requirements in the areas where the image gradient have large variations. In this dissertation, an improved restoration algorithm based on the TV model and P-Laplace algorithm is proposed, which combines the advantages of the two algorithms. Moreover, according to the characteristics of the pixel information in the areas to be restored, a diffusion parameter κ is presented to obtain a flexible transition between isotropic diffusion and anisotropic diffusion. The control parameter κ determines the choice of the restoration model according to the pixel gradient, and thus can improve the performance of image restoration.To test the performance of the proposed algorithm, the restoration results of the TV model, P-Laplace algorithm and the proposed algorithms under the same experimental conditions are compared. The four experimental images include the Lena damaged image by text, the scratch image of Lena, the photographer damaged image by text and the scratch image of photographer. And the experimental results show that the proposed algorithm obtain more satisfying restoration results than the compared algorithms. It can also be seen that the proposed algorithm combines the advantages of the TV model and P-Laplace algorithm, which can both preserve the edge information and enact isotropic diffusion in the flat areas.