Reconstruction of small and extended regions in EIT with a Robin transmission condition
Reconstruction of small and extended regions in EIT with a Robin transmission condition
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DOI：
10.1088/1361-6420/ac8b2e
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发表时间：
2022-03
期刊：
影响因子：
2.1
通讯作者：
G. Granados;I. Harris
中科院分区：
文献类型：
--
作者：
G. Granados;I. Harris
我们考虑一个逆形状问题来自电阻抗断层扫描与罗宾传输条件。通常，Robin型边界条件模拟腐蚀。本文研究了两种从静电数据中恢复内部腐蚀区域的方法。我们考虑的情况下，我们有小体积和扩展区域。对于该区域具有小体积的情况下，我们将推导出当前间隙算子的渐近展开，并证明MUSIC型算法可以用于恢复该区域。在其中一个具有扩展区域的情况下，我们将展示正则化因子分解方法可以用于恢复所述区域。数值例子将在两个维度的单位圆的情况下。
We consider an inverse shape problem coming from electrical impedance tomography with a Robin transmission condition. In general, a boundary condition of Robin type models corrosion. In this paper, we study two methods for recovering an interior corroded region from electrostatic data. We consider the case where we have small volume and extended regions. For the case where the region has small volume, we will derive an asymptotic expansion of the current gap operator and prove that a MUSIC-type algorithm can be used to recover the region. In the case where one has an extended region, we will show that the regularized factorization method can be used to recover said region. Numerical examples will be presented for both cases in two dimensions in the unit circle.