Image Theory for Electrical Impedance Tomography

Abstract

Image reconstruction by electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. Herein, we present a novel electrical impedance tomography algorithm for reconstruction of layered biological tissues with piecewise continuous plane-stratified profiles. The algorithm is based on the reconstruction scheme for piecewise constant conductivity profiles, which utilizes Legendre expansion in conjunction with improved Prony method. This reconstruction procedure, which calculates both the locations and the conductivities, repetitively provides inhomogeneous depth discretization, (i.e., the depths grid is not equispaced). Incorporation of this specific inhomogeneous grid in the widely used mean least square reconstruction procedure results in a stable and accurate reconstruction, whereas, the commonly selected equispaced depth grid leads to unstable reconstruction. This observation establishes the main result of our investigation, highlighting the impact of physical phenomenon (image theory) on electrical impedance tomography, leading to a physically motivated stabilization of the inverse problem, (i.e., an inhomogeneous depth discretization renders an inherent regularization of the mean least square algorithm).