基于广义超松弛迭代的图像复原

Image Restoration Based on Generalized Successive over Relaxation

图像复原问题常常可转化为大型线性系统的求解问题。Tikhonov正则化将线性系统求解转化为最小化问题。根据最优性条件将最小化问题转化为鞍点问题,并提出了一种求解该鞍点问题的广义超松弛迭代算法。证明了当松弛因子满足一定条件时广义超松弛迭代算法是收敛的,分析并给出了松弛因子的最优值。在2个实际图像复原问题上的数值实验结果表明,该算法较其他算法复原后图像的峰值信噪比较高、相对误差较小,是十分有效的。

Image restoration problems can often be transformed into solving problems of large linear systems.Tikhonov regularization transforms the solving problems of a linear system to a minimization problem.According to the optimality condition,the minimization problem is converted to the saddle point problem,and a generalized successive over relaxation algorithm for solving the saddle point problem is proposed.It is proved that the generalized successive over relaxation algorithm is convergent when the relaxation factor satisfies certain conditions.The optimal value of the relaxation factor is analyzed and given.The numerical experiment results on two real image restoration problems show that compared with other algorithms,such algorithm has a relatively high peak signal-to-noise ratio and small relative error after the image restoration.