Numerical solution of the coefficient inverse problem of electrical impedance tomography using laboratory measurements
https://doi.org/10.25205/1818-7900-2025-23-4-5-22
Abstract
An iterative numerical method for solving the inverse coefficient problem for a uniform elliptic equation with integro-differential boundary conditions in a closed domain is presented. The method relies on finite-volume approximations of differential and integral operators on unstructured grids, numerical solution of a sequence of direct problems with a known piecewise constant distribution of coefficients of a difference elliptic equation, and the convergent iteratively regularizable Gauss-Newton method. The developed method for solving inverse problems of electrical impedance tomography has been tested on electrical voltage measurements performed at the KIT experimental stand at the University of Eastern Finland. The results of reconstruction of electrical conductivity within the research area are close to the real ones.
Keywords
coefficient inverse problem,
elliptic equation with piecewise constant coefficients,
integro-differential boundary condition,
finite volume method,
unstructured grids,
complete electrode model,
conduction reconstruction,
iteratively regularized Gauss-Newton method
Supporting agencies: The work was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Project for the development of regional mathematical centers).
About the Authors
A. A. Afanaseva
Tomsk State University
Russian Federation
Russian Federation
Anna A. Afanaseva, Graduate Student of Department of Computational Mathematics and Computer Modelling of National Research
Tomsk
A. V. Starchenko
Tomsk State University
Russian Federation
Russian Federation
Alexander V. Starchenko, Professor, Doctor of Physical and Mathematical Sciences, Head of Department of Computational Mathematics and Computer Modelling of National Research, Scientific Researcher, Regional Scientific Educational Mathematical Center
Researcher ID B-2354-2014
Tomsk
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Review
For citations:
Afanaseva A.A., Starchenko A.V. Numerical solution of the coefficient inverse problem of electrical impedance tomography using laboratory measurements. Vestnik NSU. Series: Information Technologies. 2025;23(4):5-22. (In Russ.) https://doi.org/10.25205/1818-7900-2025-23-4-5-22
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