Interpolation of missing electrode data in electrical impedance tomography

TL;DR

This paper introduces a computationally efficient interpolation method for estimating voltage measurements on current-driven electrodes in electrical impedance tomography, enabling more practical and real-time difference EIT reconstructions.

Contribution

The authors develop a novel interpolation technique that predicts missing electrode data using prior bounds on conductivity changes, improving EIT measurement accuracy.

Findings

Interpolation method accurately predicts missing voltages.

Method enables real-time EIT reconstruction.

Feasibility demonstrated with monotonicity-based reconstruction.

Abstract

Novel reconstruction methods for electrical impedance tomography (EIT) often require voltage measurements on current-driven electrodes. Such measurements are notoriously difficult to obtain in practice as they tend to be affected by unknown contact impedances and require problematic simultaneous measurements of voltage and current. In this work, we develop an interpolation method that predicts the voltages on current-driven electrodes from the more reliable measurements on current-free electrodes for difference EIT settings, where a conductivity change is to be recovered from difference measurements. Our new method requires the a-priori knowledge of an upper bound of the conductivity change, and utilizes this bound to interpolate in a way that is consistent with the special geometry-specific smoothness of difference EIT data. Our new interpolation method is computationally cheap enough to allow for real-time applications, and simple to implement as it can be formulated with the standard sensitivity matrix. We numerically evaluate the accuracy of the interpolated data and demonstrate the feasibility of using interpolated measurements for a monotonicity-based reconstruction method.