基于平移预条件技术的改进超松弛迭代图像复原

Shiftting Precondition Technique of Modifying Successive Overrelaxation Iteration Method on Image Restoration

图像复原问题常常可转化为大型线性系统的求解问题.为解决超松弛迭代算法在求解大型稀疏线性系统时的收敛不稳定问题,提出了一种改进的超松弛迭代算法.通过平移预条件技术将超松弛迭代的迭代矩阵进行改进以避免奇异,研究了改进算法的收敛性和松弛参数的取值范围.在两个实际图像复原问题上的数值实验结果表明,改进算法是稳定和有效的.

In this paper,the problem of image restoration is often transformed into the solving large linear systems. An modified overrelaxation iterative algorithm is proposed to solve the convergence instability of the overrelaxation iterative algorithm of solving large sparse linear systems. The iterative matrix of overrelaxation iteration is improved to avoid the singularity by shiftting precondition technique. The convergence and relaxation parameters of the improved algorithm are studied. The numerical results of two actual image restoration problems show that the improved algorithm is stable and effective.