Existence and Uniqueness in Anisotropic Conductivity Reconstruction with Faraday’s Law
نویسندگان
چکیده
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 in two space dimensions. The curl free equation of Faraday’s law is taken instead of the usual divergence free equation of the electrical impedance tomography. Boundary conditions related to given current densities are introduced which complete a well determined problem for conductivity reconstruction together with Faraday’s law.
منابع مشابه
Orthotropic Conductivity Reconstruction with Virtual Resistive Network and Faraday’s Law
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 conductivity. The curl free equation of Faraday’s law is taken instead of the elliptic equation in a divergence form which is typically used in electrical impedance tomography. A reconstruction method b...
متن کاملResistivity Tensor Imaging via Network Discretization of Faraday's Law
A resistive network based anisotropic resistivity reconstruction method is introduced when three sets of internal electrical currents are given. Faraday’s law is discretized using resistive networks for an anisotropic resistivity body such as a muscle or nerve fiber structure of an animal body. The resistivity tensor imaging method of this paper may provide another approach to find the fiber st...
متن کاملVirtual Resistive Network and Conductivity Reconstruction with Faraday’s Law
Network based conductivity reconstruction method is introduced using the third Maxwell’s equation, or Faraday’s law, for a static case. The usual choice in electrical impedance tomography is the divergence free equation of the electrical current density. However, if the electrical current density is given, the curl free equation of the electrical field gives a direct relation between the curren...
متن کاملWell-posedness in anisotropic conductivity reconstruction
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 two dimensions is well-posed. This is relevant to an application of a medical diagnosis on human organism since human organism typically has an anisotropic conductivity. In the first part of thesis,...
متن کاملWell-posedness of the Conductivity Reconstruction from an Interior Current Density in Terms of Schauder Theory
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 in two space dimensions. Uniqueness for similar conductivity reconstruction problems has been known for several cases. However, the existence and the stability are obtained in this paper for the fir...
متن کامل