Orthotropic conductivity reconstruction with virtual-resistive network and Faraday's law (Q2800530)

Theoretical investigations and numerical schemes are conducted and developed for orthotropic conductivity reconstruction in two-dimensional spaces. 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. The well-posedness, including the existence and uniqueness of the direct problem involving orthotropic conductivity, i.e., the curl free equation on Faraday's law are proved by using two sets of internal current densities and boundary conductivity. Numerical reconstruction schemes are proposed based on a layered bricks type virtual resistive network. Numerical tests show that the proposed numerical reconstruction schemes are insensitive to noise, which is stable up to 40\% multiplicative noise.