Optimizing Electrode Positions in Electrical Impedance Tomography

Abstract

Abstract. Electrical impedance tomography is an imaging modality for recovering information about the conductivity inside a physical body from boundary measurements of current and voltage. In practice, such measurements are performed with a finite number of contact electrodes. This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized) conductivity, i.e., the conditional density of the conductivity given the measurements, is as localized as possible. To make such an approach computationally feasible, the complete electrode forward model of impedance tomography is linearized around the prior expectation of the conductivity, allowing explicit representation for the (approximate) posterior covariance matrix. Two approaches are considered: minimizing the trace or the determinant of the posterior covariance. The introduced optimization algorithm is of the steepest descent type, with the needed gradients computed based on appropriate Fréchet derivatives of the complete electrode model. The functionality of the methodology is demonstrated via two-dimensional numerical experiments. Key words. Electrical impedance tomography, optimal electrode locations, Bayesian inversion, complete electrode model, optimal experiment design AMS subject classifications. 65N21, 35Q60, 62F15