Abstract: Image inpainting is an important subject in the study of image restoration. In allusion to the staircase effect in the process of total variational model in restoring image, this paper introduces the high-order Partial Differential Equation（PDE） into the image inpainting, then uses the penalty method and the alternating minimization algorithm to solve it. Simulation experiments and result analysis show the effectiveness and superiority of the proposed model and algorithm.

Key words: image inpainting, total variation model, high-order model, penalty method, alternating minimization algorithm

摘要： 图像修补是图像复原研究中的一个重要课题。针对总变分模型在修补图像过程中存在的阶梯效应，将高阶偏微分方程（PDE）引入到图像修补中，采用罚方法及交替极小化算法求解该模型。通过仿真实验及结果分析说明该模型及算法的有效性和优越性。

关键词: 图像修补, 总变分模型, 高阶模型, 罚方法, 交替极小化算法