Local detection of three-dimensional inclusions in electrical impedance tomography
Local detection of three-dimensional inclusions in electrical impedance tomography
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DOI：
10.1088/0266-5611/26/3/035001
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发表时间：
2010-01
期刊：
影响因子：
2.1
通讯作者：
Takanori Ide;Hiroshi Isozaki;Susumu Nakata;S. Siltanen
中科院分区：
文献类型：
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作者：
Takanori Ide;Hiroshi Isozaki;Susumu Nakata;S. Siltanen
假设给定一个三维有界区域，内部电导率分布未知。此外，假设电导率由已知背景和未知异常区域（内含物）组成，其中电导率值未知且与背景不同。Ide等人（2007 common）介绍了一种方法。纯粹的达成。数学。60 1415-42)，用于从在物体边界进行的噪声局部电压电流测量中近似地定位内含物。该方法基于复杂几何光学解和双曲几何的使用；本文对二维情况进行了数值试验。这项工作报告了该方法在三维中计算实现的结果，其中数据的模拟和计算机化反演算法都比在二维中更复杂。该算法增加了三个新的正则化步骤，显著提高了对噪声的鲁棒性。数值实验结果表明，在具有实际测量噪声水平的数据中，可以可靠地恢复夹杂物的大致位置。该结果的潜在应用包括乳腺癌的早期诊断、地下污染物检测和无损检测。
Assume one is given a three-dimensional bounded domain with an unknown conductivity distribution inside. Further, suppose that the conductivity consists of a known background and unknown anomalous regions (inclusions) where conductivity values are unknown and different from the background. A method is introduced in Ide et al (2007 Commun. Pure Appl. Math. 60 1415–42) for locating inclusions approximately from noisy localized voltage-to-current measurements performed at the boundary of the body. The method is based on the use of complex geometrical optics solutions and hyperbolic geometry; numerical testing is presented in the aforementioned paper for the two-dimensional case. This work reports the results of computational implementation of the method in dimension three, where both the simulation of data and the computerized inversion algorithm are more complicated than in dimension two. Three new regularizing steps are added to the algorithm, resulting in significantly better robustness against noise. Numerical experiments are reported, suggesting that the approximate location of the inclusions can be reliably recovered from the data with a realistic level of measurement noise. Potential applications of the results include early diagnosis of breast cancer, underground contaminant detection and nondestructive testing.