论文标题
与建模误差的电阻抗层析成像的串联归还
Series reversion for electrical impedance tomography with modeling errors
论文作者
论文摘要
这项工作扩展了[Garde和Hyvönen，Math的结果。 comp。 91：1925-1953]关于Calderón对逼真的电极测量问题的串联恢复，并在被调查的机构的内部入场性和在电极对象接口处的接触式入学率都被视为未知。向前的操作员将内部和触点入口发送到线性电极电流到电位映射，首先被证明是分析性的。相应的泰勒系列的归还产生了一个数值方法的家族，这些方法是解决电阻抗断层扫描的反向问题，有可能对未知的内部和边界入学使用不同的参数化。仅当未知数的使用有限维参数化允许向前映射的Fréchet导数具有侵入性时，才能建立方法的功能和收敛性，但是我们还通过诉诸于贝耶斯式倒置动机的正则化来将方法扩展到更一般的设置。这种正规化方法的性能通过基于模拟数据的三维数值示例测试。建模与电极形状和接触入学相关的误差的效果是数值研究的焦点。
This work extends the results of [Garde and Hyvönen, Math. Comp. 91:1925-1953] on series reversion for Calderón's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and the contact admittivity at the electrode-object interfaces treated as unknowns. The forward operator, sending the internal and contact admittivities to the linear electrode current-to-potential map, is first proven to be analytic. A reversion of the corresponding Taylor series yields a family of numerical methods of different orders for solving the inverse problem of electrical impedance tomography, with the possibility to employ different parametrizations for the unknown internal and boundary admittivities. The functionality and convergence of the methods is established only if the employed finite-dimensional parametrization of the unknowns allows the Fréchet derivative of the forward map to be injective, but we also heuristically extend the methods to more general settings by resorting to regularization motivated by Bayesian inversion. The performance of this regularized approach is tested via three-dimensional numerical examples based on simulated data. The effect of modeling errors related to electrode shapes and contact admittances is a focal point of the numerical studies.
