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The objective of electrical impedance tomography is to reconstruct theinternal conductivity of a physical body based on measurements of current andpotential at a finite number of electrodes attached to its boundary. Althoughthe conductivity is the quantity of main interest in impedance tomography, areal-world measurement configuration includes other unknown parameters as well:the information on the contact resistances, electrode positions and body shapeis almost always incomplete. In this work, the dependence of the electrodemeasurements on all aforementioned model properties is parametrized viapolynomial collocation. The availability of such a parametrization enablesefficient simultaneous reconstruction of the conductivity and other unknowns bya Newton-type output least squares algorithm, which is demonstrated bytwo-dimensional numerical experiments based on both noisy simulated data andexperimental data from two water tanks.

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