图像修复TV模型的快速算法研究

摘要

There are many ways in solving the Total Variation ( TV) model for image inpainting. For total variation model of image in-painting which contains non-smooth convex optimization problems,a fast solving algorithm on Alternating Direction Method of Multipli-ers ( ADMM) is presented. Generally,the Gauss-Seidel method is usually used for iterative formula in specific sub-problems. In this pa-per,by analyzing the feature of TV model,improve the ADMM,so that can use the fast Fourier transform methods to solve specific prob-lems. Then the convergence of the algorithm is proved. Experimental results show that the new algorithm presented in this paper is not on-ly better in inpainting,but also faster.%关于图像修复的全变分( TV)模型的求解有很多方法。在图像修复的全变分( TV)模型中，文中针对含有非光滑项的凸优化问题提出了一种基于交替方向乘子法( ADMM)的快速求解算法。 ADMM方法对迭代公式中具体的子问题求解过程一般采用Gauss-Seidel方法，文中通过分析TV修复模型的性质，对ADMM算法进行了相应的改进，使得具体的数值求解可以用快速傅里叶变换方法，并证明了该算法的收敛性。实验结果表明，文中所提出的新算法与采用Gauss-Seidel迭代的方法相比较，不但修复效果更好，而且修复速度更快。