A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography
A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography
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DOI：
10.1016/j.jcp.2022.111862
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Cuiyang Ding;Yijing Zhou;W. Cai;Xuan Zeng;Changhao Yan
中科院分区：
文献类型：
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作者：
Cuiyang Ding;Yijing Zhou;W. Cai;Xuan Zeng;Changhao Yan
提出了一种基于Feynman-Kac公式的路径积分Monte Carlo方法（PIMC），用于求解具有混合边界条件的拉普拉斯方程的电阻抗断层成像（EIT）正问题。正问题是EIT逆问题迭代算法的重要组成部分，而所提出的PIMC提供了一个局部的解决方案来找到单个电极上的电势和电流。本文提出了改进的方法，以更高的精度计算拉普拉斯方程混合边值问题的反射布朗运动的局部时和Feynman-Kac公式。用该方法求解混合边界问题，得到了八电极三维EIT模型电极上精确的电压-电流图。
A path integral Monte Carlo method (PIMC) based on a Feynman-Kac formula for the Laplace equation with mixed boundary conditions is proposed to solve the forward problem of the electrical impedance tomography (EIT). The forward problem is an important part of iterative algorithms of the inverse EIT problem, and the proposed PIMC provides a local solution to find the potentials and currents on individual electrodes. Improved techniques are proposed to compute with better accuracy both the local time of reflecting Brownian motions (RBMs) and the Feynman-Kac formula for mixed boundary problems of the Laplace equation. Accurate voltage-to-current maps on the electrodes of a model 3-D EIT problem with eight electrodes are obtained by solving a mixed boundary problem with the proposed PIMC method.