Nonstationary Shape Estimation in Electrical Impedance Tomography Using a Parametric Level Set-Based Extended Kalman Filter Approach

This paper presents a parametric level set-based reconstruction method for nonstationary applications using electrical impedance tomography (EIT). Due to relatively low signal-to-noise ratios in EIT measurement systems and the diffusive nature of EIT, the reconstructed images often suffer from low spatial resolution. In addressing these challenges, we propose a computationally efficient shape-estimation approach where the conductivity distribution to be reconstructed is assumed to be piecewise constant, and the region boundaries are assumed to be nonstationary in the sense that the characteristics of region boundaries change during measurement time. The EIT inverse problem is formulated as a state estimation problem in which the system is modeled with a state equation and an observation equation. Given the temporal evolution model of the boundaries and observation model, the objective is to estimate a sequence of states for the nonstationary region boundaries. The implementation of the approach is based on the finite-element method and a parametric representation of the region boundaries using level set functions. The performance of the proposed approach is evaluated with the simulated examples of thorax imaging, using noisy synthetic data and experimental data from a laboratory setting. In addition, robustness studies of the approach with respect to the modeling errors caused by inaccurately known boundary shape, non-homogeneous background and varying conductivity values of the targets are carried out and it is found that the proposed approach tolerates such kind of modeling errors, leading to good reconstructions in nonstationary situations.