An Investigation of Modeling Error of EIT Reconstruction

Abstract

Electrical Impedance Tomography is an imaging method which attempts to reveal the conductivity distribution of a domain based on the electrical boundary condition. For time difference EIT, the voltage difference at two time steps is employed for reconstruction. This is an ill-posed inverse problem, especially, it is non-linear. The currently available EIT devices are all based on linearized reconstruction algorithms. The linearized reconstruction employs a reconstruction matrix which is essentially a regularized pseudo inverse of the Jacobian matrix. This reconstruction matrix multiplying the voltage differences will provide a distribution of conductivity changes. However, the linearized reconstruction contains modelling error. In this paper, we study the modelling error caused by linearization based on the shunt model through simulations. Specifying a current injection pattern in simulation, at each time step a simulated voltage measurement can be calculated from Maxwell’s equations. The voltage difference between two time steps can be obtained. On the other hand, according to the assumption of linearized reconstruction, the voltage difference is assumed to be the Jacobian matrix multiplying the conductivity distribution changes. The discrepancy between these two voltage differences will be studied.