基于改进共轭梯度法的ERT图像重建

ERT image reconstruction based on improved CG method

针对电阻层析成像(ERT)图像重建中灵敏度矩阵的病态特性导致共轭梯度法的收敛率低的问题,提出了改进的共轭梯度算法,ERT图像重建前先对数据进行归一化预处理,将解空间映射到Krylov子空间中,再通过共轭梯度法求解低维子空间中的反问题。分别利用共轭梯度法、预处理共轭梯度法和改进共轭梯度法对典型的气水两相流模型做了仿真实验。实验结果表明,改进共轭梯度法能够提高重建图像的质量,并且相对于其他算法,降低了计算时间。

Aimingat the problem that the ill-posed property of the sensitivity matrix in Electrical Resistance Tomography（ ERT） image reconstructionleads to the low convergence rate of the Conjugate Gradient（ CG） method,animproved CG algorithmis proposed in this paper. Before ERT image reconstruction,normalized pre-processing is conducted on theexperiment data; the solution space is projected into the Krylov subspace. Then,the inverse problem in the low dimensional specific subspace is solved with CG method. Typical gaswater two-phase flow simulation models were constructed,and the CG method,preprocessing CG method and improved CG algorithm were used to conduct image reconstruction experiments on the simulation models. The experiment results show that the improved CG algorithm can improve the reconstruction imagequality andreduce the computing time compared with other algorithms.