Resistor network approaches to electrical impedance tomography
Resistor network approaches to electrical impedance tomography
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发表时间：
2011-07
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通讯作者：
L. Borcea;V. Druskin;F. G. Vasquez;A. Mamonov
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作者：
L. Borcea;V. Druskin;F. G. Vasquez;A. Mamonov
本文综述了电阻网络法在电阻抗断层成像（EIT）逆问题数值求解中的应用。网络出现在有限体积离散的椭圆方程的电势，稀疏和自适应细化网格，我们称之为最佳的上下文中。这个名字指的是这样一个事实，即网格给出了Dirichlet到Neumann映射的光谱精确近似，EIT中的数据。最优网格反演的基本特点是将电阻网络的离散反问题与连续EIT问题联系起来。
We review a resistor network approach to the numerical solution of the inverse problem of electrical impedance tomography (EIT). The networks arise in the context of finite volume discretizations of the elliptic equation for the electric potential, on sparse and adaptively refined grids that we call optimal. The name refers to the fact that the grids give spectrally accurate approximations of the Dirichlet to Neumann map, the data in EIT. The fundamental feature of the optimal grids in inversion is that they connect the discrete inverse problem for resistor networks to the continuum EIT problem.