基于拉普拉斯算子和图像修补的图像去噪算法

摘要

通过分析偏微分方程(PDE),设计了基于拉普拉斯算子和图像修补的图像去噪算法用于处理被噪声污染的图像:ROF调和拉普拉斯(RHL)算法和ROF调和修补(RHI)算法.通过分析图像的局部特征,结合ROF模型在处理图像时具有边缘保护能力,调和模型在处理图像平滑区域时能够避免产生“阶梯效应”和拉普拉斯算子具有增强细节信息的特点,设计了RHL算法；在RHL算法的基础上,结合基于PDE的图像修补模型设计了RHI算法.实验结果表明,设计的RHL算法和RHI算法既克服了ROF模型、调和模型在去除图像噪声时的缺点,又结合了两者的优点,与其他基于PDE的算法相比,在去除图像噪声、处理图像平滑区域、保持图像边缘细节信息方面都有较好的性能.%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.