Nonlinear integral equations for the inverse electrical impedance problem
Nonlinear integral equations for the inverse electrical impedance problem
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DOI：
10.1088/0266-5611/23/2/002
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发表时间：
2007-04
期刊：
影响因子：
2.1
通讯作者：
H. Eckel;R. Kress
中科院分区：
文献类型：
--
作者：
H. Eckel;R. Kress
本文研究了电导率为分段常数的二维电阻抗反问题。我们的方法是基于一个系统的非线性积分方程的未知形状的子域的恒定电导率和未知的电导率迭代通过线性化。我们的方法扩展了Kress和Rundell（2005年逆问题21 1207-23）提出的方法，为一个完美的情况下进行的夹杂物。对于算法中正则化参数的选择，我们提出了一种进化算法，并通过采用因式分解方法获得迭代的初始猜测。我们详细描述了该方法，并通过数值例子说明其可行性。
We consider the two-dimensional inverse electrical impedance problem in the case of piecewise constant conductivities. Our approach is based on a system of nonlinear integral equations from which the unknown shapes of the subdomains with constant conductivity and the unknown conductivities are obtained iteratively via linearization. Our approach extends a method that has been suggested by Kress and Rundell (2005 Inverse Problems 21 1207–23) for the case of a perfectly conducting inclusion. For the choice of the regularization parameters occurring in the algorithm we suggest an evolutionary algorithm and the initial guess for the iterations is obtained through employing the factorization method. We describe the method in detail and illustrate its feasibility by numerical examples.