电容层析成像系统图像重建算法的研究

本文利用Tikhonov正则化和奇异系统理论,分析了引起电容层析成像系统逆问题不适定性的根本原因是由于敏感场矩阵小奇异值的存在。针对一般Tikhonov正则化方法将所有的奇异值都采取同一正则化参数修正带来的误差,本文将小奇异值对应的项设定正则化参数,而舍去零奇异值对应向量,既减少了误差又加快了速度。例算结果表明,用本文方法重建图像,比其它如线性反投影算法(LBP)、Landweber迭代法及一般Tikhonov正则化算法,都有一定程度的改善。

Study on Image Reconstruction Algorithm for Electrical Capacitance Tomography System

Based on Tikhonov regularization and singular system theory, it is analyzed that the cause of the ill- posed characteristic of the inverse problem in electrical capacitance tomography system is due to the small singular values of the sensitivity distribution ma- trix. Differ from the conventional technique in Tikhonov regularization method that all the singular values are modified with the same parameter, which will result in more solution error, a new technique is proposed in this paper, in which small singular values except the zeros are manipulated by the regularization. Less solution error and rapider solving procedure can achieved by using this tech- nique. Numerical experiments show that the proposed method can provide images superior to those reconstructed by the linear back projection (LBP), Landweber iterative method and the standard Tikhonov regularization method.