A nonlinear approach to difference imaging in EIT; assessment of the robustness in the presence of modelling errors

Abstract

Electrical impedance tomography (EIT) is highly sensitive to modelling errors that arise from model reductions and inaccurate knowledge of auxiliary model parameters such as electrode positions, contact impedances and boundary shape of the body. In difference imaging, where the objective is to reconstruct change in the conductivity between EIT measurements at two time instants, the traditional way to circumvent modelling errors is to reconstruct the conductivity change using difference of the measurements and a global linearization of the nonlinear forward problem. Recently, a nonlinear reconstruction approach for difference imaging was proposed (Liu et al 2015 Inverse Probl. Imaging 9, in press). The key feature of the approach is to parameterize the conductivity after the change as a linear combination of the initial conductivity and the conductivity change, and then estimate the initial conductivity and conductivity change by minimizing regularized least squares formulation based on both data sets. This approach allows independently modelling the spatial characteristics of the initial conductivity and the conductivity change by applying separate regularization functionals. In this paper, we investigate how well the nonlinear approach tolerates modelling errors and compare the reconstructions to the results with traditional linearized reconstruction method. The robustness is studied in cases of modelling errors arising from domain truncation, unknown contact impedances, inaccurately known electrode locations and inaccurately known domain boundary using simulated and experimental EIT data.