基于主元加权和自控步长的反演成像联合迭代法

摘要

为提高弹性波CT层析成像中反演成像的质量，同时考虑到反演成像过程中系数矩阵的病态性，提出了基于主元加权和自控步长的联合迭代法（HSIRT算法）。该方法通过对原方程组系数矩阵进行降条件数主权加元预处理，再与基于范数收敛性构造的自控步长迭代格式相结合进行求解。通过数值模拟和预制含缺陷的方钢管混凝土构件进行试验检测，结果表明HSIRT算法较SIRT算法具有更好的收敛速度和精度；求得的无缺陷区波速更为平稳，无缺陷区与缺陷区波速差距更为明显；对缺陷的辨识度更高，成像效果更好。%To improve the accuracy of inversion imaging in elastic wave CT, a new technique based on weighted PCA for si-multaneous iterative reconstruction with automatically controlled steps is proposed considering the morbidity of coefficient matrix in counting process. The coefficient matrix of the original equations was preproceed through reducing condition numbers of weighted PCA,and then solve the equations cooperating with the iterative formula was solved with automatically controlled steps based on norm convergence structure. Proved by the numerical simulation and model tests,the new algorithm has such advantages as better speed, precision on convergence, more smooth wave velocity in the no-defect area, wave velocity difference between defect area, no-defect area ensured higher identification for defect and better image quality.