用于电容层析成像技术的共轭梯度算法

Conjugate Gradient Algorithm for Electrical Capacitance Tomography

针对电容层析成像技术中的“软场”效应和病定问题,基于灵敏度矩阵的奇异值分解理论,提出共轭梯度图像重建算法及其改进算法———正则化共轭梯度法.仿真实验得知:经过 200次迭代后,Landweber算法残差为0. 139 5,未加正则化的共轭梯度算法残差为 1. 357 7×10-4;完成同样操作,Landweber算法迭代耗时 9. 3s,共轭梯度法只需 6. 8s.可见,共轭梯度法是一种比其他的迭代算法收敛更快、成像效果更好的图像重建算法.

To solve the “soft-field” nature and the ill-posed problem in electrical capacitance tomography technology,the conjugate gradient image reconstruction method and its modified method(i.e. regularized conjugate gradient method) are presented based on the singular decomposition theory of the sensitivity matrix. Simulated test shows that through 200 times iterations the residual and computing time are 0.139 5 and 9.3 s respectively for Landweber algorithm,but that are 1.357 7×10^(-4) and 6.8 s respectively for conjugate gradient method without regularization.It is thus clear that conjugate gradient method can provide images superior to those obtained with the linear back projection (LBP) and Landweber iterative algorithm and other image reconstruction methods.