Recovering conductivity at the boundaryin three-dimensional electrical impedance tomography

Gen Nakamura; Päivi Ronkanen; Samuli Siltanen; Kazumi Tanuma

doi:10.3934/ipi.2011.5.485

Article Contents

2011, Volume 5, Issue 2: 485-510. Doi: 10.3934/ipi.2011.5.485

This issue Previous Article Near field sampling type methods for the inverse fluid--solid interaction problem Next Article Non-local regularization of inverse problems

Recovering conductivity at the boundary in three-dimensional electrical impedance tomography

1.
Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810
2.
Department of Physics and Mathematics, University of Eastern Finland, FIN-70211 Kuopio
3.
University of Helsinki, Department of Mathematics and Statistics, FI-00014 Helsinki
4.
Department of Mathematics, Graduate School of Engineering, Gunma University, Kiryu 376-8515

Received: March 31, 2010

Revised: July 31, 2010

Published: April 2011

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Abstract

The aim of electrical impedance tomography (EIT) is to reconstruct the conductivity values inside a conductive object from electric measurements performed at the boundary of the object. EIT has applications in medical imaging, nondestructive testing, geological remote sensing and subsurface monitoring. Recovering the conductivity and its normal derivative at the boundary is a preliminary step in many EIT algorithms; Nakamura and Tanuma introduced formulae for recovering them approximately from localized voltage-to-current measurements in [Recent Development in Theories & Numerics, International Conference on Inverse Problems 2003]. The present study extends that work both theoretically and computationally. As a theoretical contribution, reconstruction formulas are proved in a more general setting. On the computational side, numerical implementation of the reconstruction formulae is presented in three-dimensional cylindrical geometry. These experiments, based on simulated noisy EIT data, suggest that the conductivity at the boundary can be recovered with reasonable accuracy using practically realizable measurements. Further, the normal derivative of the conductivity can also be recovered in a similar fashion if measurements from a homogeneous conductor (dummy load) are available for use in a calibration step.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 65N21.

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