Simulation of error propagation in finite element image reconstruction for electrical impedance tomography

Using extensimulations, we have investigated the behaviour of finite element image reconstruction for electrical impedance tomography in the presence of inaccuracies likely to exist in real measurements. This study characterizes reconstruction when subjected to noise propagation using different excitation patterns and modes of operation. Specifically, a generalized framework for finite element image reconstruction is presented which allows electrical impedance images to be recovered from data collected in either voltage, current or impedance modes of operation that correspond naturally to the allowable boundary condition types which determine unique model solutions to the underlying partial differential equation as the basis for property estimation. Driving conditions consisting of electrode pairs, trigonometric or synthesized trigonometric patterns have been considered. The simulations presented here are based on an arbitrary impedance distribution for which applied and observed voltages and currents were computed. The applied and observed patterns were then processed identically to real data with the addition of 0, 0.1% and 1% random Gaussian noise. The mean squared error (MSE) between the reconstructed and exact impedance images constituted the measure of algorithmic performance. Our findings suggest that finite element reconstruction tolerates noise on the measurement data better than on the applied portion of the signal; pair excitations consistently produced the lowest MSE: noise appears to compound itself in the synthesized trigonometric patterns mode, and the applied voltage mode consistently yields more accurate images in the presence of noise than the equivalent cases corresponding to current mode. While only evaluated with trigonometric patterns. the impedance mode generally produced the lowest MSE in a limited set of simulation comparisons.