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 that is typically used in electrical impedance tomography. A reconstruction method based on layered bricks-type virtual-resistive network is developed to reconstruct orthotropic conductivity with up to 40% multiplicative noise.