Polynomial collocation for handling an inaccurately known measurement configuration in electrical impedance tomography

TL;DR

This paper introduces a polynomial collocation approach to jointly reconstruct internal conductivity and unknown measurement configuration parameters in electrical impedance tomography, improving robustness to model inaccuracies.

Contribution

It presents a novel polynomial collocation parametrization for measurement configuration uncertainties, enabling simultaneous reconstruction with a Newton-type algorithm.

Findings

Effective reconstruction with noisy data demonstrated

Numerical experiments validate the method's robustness

Applicable to real experimental data from water tanks

Abstract

The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the conductivity is the quantity of main interest in impedance tomography, a real-world measurement configuration includes other unknown parameters as well: the information on the contact resistances, electrode positions and body shape is almost always incomplete. In this work, the dependence of the electrode measurements on all aforementioned model properties is parametrized via polynomial collocation. The availability of such a parametrization enables efficient simultaneous reconstruction of the conductivity and other unknowns by a Newton-type output least squares algorithm, which is demonstrated by two-dimensional numerical experiments based on both noisy simulated data and experimental data from two water tanks.