Artificial boundary conditions and domain truncation in electrical impedance tomography. Part II: Stochastic extension of the boundary map

Daniela  Calvetti; Paul J.  Hadwin; Janne M. J.  Huttunen; Jari P.  Kaipio; Erkki  Somersalo

doi:10.3934/ipi.2015.9.767

Article Contents

2015, Volume 9, Issue 3: 767-789. Doi: 10.3934/ipi.2015.9.767

This issue Previous Article Artificial boundary conditions and domain truncation in electrical impedance tomography. Part I: Theory and preliminary results Next Article PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem

Artificial boundary conditions and domain truncation in electrical impedance tomography. Part II: Stochastic extension of the boundary map

1.
Case Western Reserve University, Department of Mathematics, Applied Mathematics, and Statistics, Cleveland, OH 44106
2.
University of Auckland, Department of Mathematics, Auckland
3.
University of Eastern Finland, Department of Applied Physics, Kuopio

Received: April 2014

Revised: January 2015

Published: August 2015

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Abstract

In [3], the authors discussed the electrical impedance tomography (EIT) problem, in which the computational domain with an unknown conductivity distribution comprises only a portion of the whole conducting body, and a boundary condition along the artificial boundary needs to be set so as to minimally disturbs the estimate in the domain of interest. It was shown that a partial Dirichlet-to-Neumann operator, or Steklov-Poincaré map, provides theoretically a perfect boundary condition. However, since the boundary condition depends on the conductivity in the truncated portion of the conductive body, it is itself an unknown that needs to be estimated along with the conductivity of interest. In this article, we develop further the computational methodology, replacing the unknown integral kernel with a low dimensional approximation. The viability of the approach is demonstrated with finite element simulations as well as with real phantom data.

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Mathematics Subject Classification: Primary: 35J20, 35R30, 65M32, 65M55, 65C60.

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