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

Abstract

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. Copyright © 2015 John Wiley & Sons, Ltd.

Avaliação de 3 diferentes aproximações para a solução do problema direto da tomografia de impedância elétrica

“…However for a current problem, (12) gives us three equations with two unknowns u and σ. Thus for a real-valued σ, this is an over-determined problem.…”

“…In this section we will show the well-posedness of the inverse problem of finding r that satisfies (13)(14) for given F and r 0 .…”

“…Since the reconstruction process is based on two equations, an iteration method has been used. However, (3) is only a linear problem for r. See [11,12,13,14,15] for further conductivity reconstruction studies based on the curl equation.…”

“…We take a divergence on (12) and obtain a single and linear equation for σ. This applies in any dimension.…”

“…The formulation of the theory is given with admissibility condition, Definition 1. Even though this paper is for the simplest case of two dimensional isotropic conductivity, the idea of using the curl free equation is extended to orthotropic or anisotropic cases (see [11,12,13]). The use of the curl free equation provides a new discretization method based on loop integrals, which has been developed into a network method (see [14]).…”