Approximation Errors in Electrical Impedance Tomography – An Experimental Study

A. Nissinen, L. M. Heikkinen and J. P. Kaipio

Department of Applied physics, University of Kuopio, P.O.Box 1627, FIN-70211 Kuopio, Finland.

Email: Antti.Nissinen@uku.fi

ABSTRACT

Image reconstruction in electrical impedance tomography (EIT) is an ill-posed non-linear inverse problem. Because of the ill-posedness, estimation of the conductivity distribution is sensitive to measurement errors (noise) and modeling errors. The measurement errors are a more extensively studied subject than the modeling errors. Typical modeling errors in EIT are incorrect modeling of the geometry of the object, discretization errors, and errors due to poorly known contact impedances. Particularly, in three-dimensional cases fine discretization leads to long computation time. Furthermore, in some cases it can be impossible to use sufficiently dense mesh because of high computer memory requirements. In practise, we have to use coarser discretization which may cause errors to the estimated conductivity distribution. In modeling error theory statistical properties of the modeling error are estimated. The enhanced error model uses both the statistics of the measurement error and the modeling error. The advantage of the modeling error theory is that we can use reduced forward problem solvers, but still use information from the accurate model. In this paper, modeling error theory is applied to two test cases (discretization errors and geometrical modeling errors). This is the first time that the modeling error approach has been used with real data. It can be seen that the enhanced error model improves the image quality significantly.

Keywords electrical impedance tomography, modeling error, inverse problem