A regularized weighted least gradient problem for conductivity imaging
A regularized weighted least gradient problem for conductivity imaging
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DOI：
10.1088/1361-6420/aaf2fd
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发表时间：
2018-04
期刊：
影响因子：
2.1
通讯作者：
A. Tamasan;A. Timonov
中科院分区：
文献类型：
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作者：
A. Tamasan;A. Timonov
我们提出并研究了一种方法，从一个内部电流密度场的大小成像的近似电导率没有任何知识的边界电压电位。仅根据该内部数据，不可能恢复确切的电导率，因为存在非唯一的解决方案。我们提出了一种方法来恢复最小残差型的解决方案。该方法是基于一个加权最小梯度问题的有界变化的平方可积迹的函数的子空间。我们证明了一个邻近问题的存在唯一性，并研究了一个正则化问题的连续依赖数据。数值实验证明了该方法的计算有效性和数值收敛性。
We propose and study a method for imaging an approximate electrical conductivity from the magnitude of one interior current density field without any knowledge of the boundary voltage potential. Solely from this interior data, the exact conductivity is impossible to recover as non-unique solutions exist. We propose a method to recover a minimum residual type solution. The method is based on a weighted least gradient problem in the subspace of functions of bounded variations with square integrable traces. We prove existence and uniqueness for a nearby problem, and study the continuous dependence data for a regularized problem. The computational effectiveness and numerical convergence of this method is demonstrated in numerical experiments.