On discretization of the depth dimension in electrical impedance tomography problems

Image reconstruction in electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. In this paper we present a case study, which uses a novel electrical impedance tomography method for reconstruction of layered biological tissues with piece-wise continuous plane-stratified profiles. The algorithm implements the recently proposed reconstruction scheme for piecewise constant conductivity profiles, based on an improved Prony method in conjunction with Bessel transform. It is shown that the proposed algorithm is capable of successfully reconstructing piece-wise continuous conductivity profiles with moderate (WKB) slop. This reconstruction procedure, which calculate 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, the main result of our investigation, in the widely used MLS reconstruction procedure results in a stable reconstruction, whereas, utilization of equispaced depth grid leads to inaccurate reconstruction. The effectiveness and the significance of inhomogeneous discretization in EIT reconstruction procedure is further demonstrated and verified via numerical simulations.