Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography

Abstract

Inverse problems can be characterized as problems that tolerate measurement and modelling errors poorly. Typical sources of modelling errors include (pure) approximation errors related to numerical discretization, unknown geometry and boundary data, and possibly sensor locations. With electrical impedance tomography (EIT), the unknown contact impedances are an additional error source. Recently, a Bayesian approach to the treatment of approximation and modelling errors for inverse problems has been proposed. This approach has been shown to be applicable to a variety of modelling and approximation errors, at least with simulations. Recently, it was shown that recovery from significant model reduction and moderate mismodelling of geometry in EIT was also possible with laboratory EIT data. In this paper, we show that the errors due to the unknown contact impedances can also be compensated for by employing the approximation error approach. Furthermore, the recovery from simultaneous contact impedance, domain truncation and discretization-related errors is also feasible.

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