中文摘要：

基于PDE（Partial Differential Equation）的图像修复因其所具有的局部自适应特性、形式上的规范性和模型建立的灵活性而受到关注,而如何在有效的进行修复受损图像的同时很好的保留图像的细节信息成为图像修复所追求的目标.本文首先对TV（total variation）模型进行了分析和讨论,针对TV模型在图像修复时会对图像过度平滑、容易丢失细节信息等问题提出了一种改进模型,该模型通过对非线性扩散项引入方向梯度和边缘引导函数,自适应的调整了模型在图像边缘和区域信息丰富区域的平滑力度;通过计算每一次迭代时待修复点33邻域内的各向灰度差分,确定最小灰度差分的方向,从而确定了该点邻域内的图像纹理走向.本文模型克服了TV模型的弱点,在有效进行破损图像修复的同时,很好的保持了边缘和纹理细节信息.通过峰值信噪比和归一化均方误差的统计结果验证了所提模型的稳定性和有效性.

英文摘要：

Image Inpainting based on the partial differential equation（PDE） has received considerable attention because it has the local self-adapting characteristics,formal normalization,and modeling flexibility.However,how to effectively repair the image as well as keep details of image is the pursued goal of image inpainting.In this paper,we firstly analyzes and discusses the TV-model,on this basic,proposes an improved model,which introduces direction gradient and guide-function of edge into the non-linear diffusion parts and adaptively adjusts the smooth intensity of the model in edge and texture information-rich regions of images;by calculating the gray level difference of the repaired point in the 33 neighborhood by each iteration to determine the direction of the smallest gray difference,so we can determine the direction of the image texture point in the neighborhood.This model not only overcomes over smoothness produced in the TV-model,but also avoids losing details and information,and greatly maintain a good image of the edge and texture details.Experimental results illustrate the effectiveness and stability of the proposed model by PSNR and NMSE.