# Virtual resistive network and conductivity reconstruction with Faradayʼs law

@article{Lee2014VirtualRN, title={Virtual resistive network and conductivity reconstruction with Faradayʼs law}, author={Min Gi Lee and Min-Su Ko and Yong-Jung Kim}, journal={Inverse Problems}, year={2014}, volume={30} }

A network-based conductivity reconstruction method is introduced using the third Maxwell equation, or Faradayʼs law, for a static case. The usual choice in electrical impedance tomography is the divergence-free equation for the electrical current density. However, if the electrical current density is given, the curl-free equation for the electrical field gives a direct relation between the current and the conductivity and this relation is used in this paper. Mimetic discretization is applied to…

## 6 Citations

### Orthotropic conductivity reconstruction with virtual‐resistive network and Faraday's law

- Mathematics
- 2016

We obtain the existence and the uniqueness at the same time in the reconstruction of orthotropic conductivity in two‐space dimensions by using two sets of internal current densities and boundary…

### Resistivity Tensor Imaging via Network Discretization of Faraday's Law

- GeologySIAM J. Imaging Sci.
- 2017

The resistivity tensor imaging method of this paper may provide another approach to finding the fiber structure of white matter by taking three sets of internal electrical current density and a part of boundary conductivity to construct the anisotropic conductivity in two space dimensions.

### Existence and uniqueness in anisotropic conductivity reconstruction with Faraday's law

- Mathematics
- 2015

Abstract. We show that three sets of internal current densities are the right amount of data that give the existence and the uniqueness at the same time in reconstructing an anisotropic conductivity…

### Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory

- Mathematics
- 2015

We show the well-posedness of the conductivity image reconstruction problem with a single set of interior electrical current data and boundary conductivity data. Isotropic conductivity is considered…

### Conductivity Recovery from One Component of the Current Density

- Mathematics
- 2014

We prove global injectivity and H\"older stability in the reconstruction of an isotopic conductivity in the electrostatic approximation of Maxwell's equations, from the information of one voltage at…

### Well-posedness in anisotropic conductivity reconstruction

- Mathematics
- 2014

In the thesis, interior conductivity reconstruction problems inferring from the interior current density data are considered. It is our main result that an anisotropic conductivity reconstruction in…

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