The Inverse Conductivity Problem with an Imperfectly Known Boundary

We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks exact knowledge of the boundary. Because of this, the numerical reconstruction from the measured EIT data is done using a model domain that represents the best guess for the true domain. However, it has been noticed that an inaccurate model of the boundary causes severe errors for the reconstructions. We introduce a new algorithm to find a deformed image of the original isotropic conductivity based on the theory of Teichmüller spaces, and we implement it numerically.