关键词: 偏微分方程, 拉普拉斯算子, 图像去噪, ROF模型, 调和模型

Abstract: Through the analysis of Partial Differential Equation (PDE), the image denoising algorithms based on Laplacian operator and image inpainting were designed for the processing of the polluted image by noise: Rudin-Osher-Fatemi (ROF) harmonical Laplacian algorithm and ROF harmonical inpainting algorithm, which were simply called RHL and RHI respectively. By analyzing the local features of the image, the ability of the ROF model in protecting image edges and the harmonical model in overcoming the "ladder effect", and the advantages of the Laplacian operator in enhancing edges, the first image denoising algorithm, RHL was designed. Meanwhile, the second algorithm RHI was designed by syncretizing the image inpainting model. The experimental results show that the two designed algorithms, RHL and RHI, have better performance visually and quantitatively than other algorithms, which combine the advantages of the ROF model and harmonical model in image denoising effectively. Compared with other PDE based algorithms, the two designed algorithms can remove noise, protect smooth region and edge information much better.

Key words: Partial Differential Equation (PDE), Laplacian operator, image denoising, Rudin-Osher-Fatemi （ROF） model, harmonical model