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Inverse Problems and Imaging (IPI)
 

Fine-tuning electrode information in electrical impedance tomography

Pages: 399 - 421, Volume 6, Issue 3, August 2012      doi:10.3934/ipi.2012.6.399

 
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Jérémi Dardé - Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland (email)
Harri Hakula - Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland (email)
Nuutti Hyvönen - Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland (email)
Stratos Staboulis - Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland (email)

Abstract: Electrical impedance tomography is a noninvasive imaging technique for recovering the admittivity distribution inside a body from boundary measurements of current and voltage. In practice, impedance tomography suffers from inaccurate modelling of the measurement setting: The exact electrode locations and the shape of the imaged object are not necessarily known precisely. In this work, we tackle the problem with imperfect electrode information by introducing the Fréchet derivative of the boundary measurement map of impedance tomography with respect to the electrode shapes and locations. This enables us to include the fine-tuning of the information on the electrode positions as a part of a Newton-type output least squares reconstruction algorithm; we demonstrate that this approach is feasible via a two-dimensional numerical example based on simulated data. The impedance tomography measurements are modelled by the complete electrode model, which is in good agreement with real-life electrode measurements.

Keywords:  Electrical impedance tomography, Fréchet derivative, domain derivative, model inaccuracies, output least squares, complete electrode model.
Mathematics Subject Classification:  35R30, 35J25, 65N21.

Received: July 2011;      Revised: May 2012;      Available Online: September 2012.

 References