Electron. J. Differential Equations, Vol. 2020 (2020), No. 93, pp. 1-30.

Existence of solution for a segmentation approach to the impedance tomography problem

Renier Mendoza, Stephen Keeling

Abstract:
In electrical impedance tomography (EIT), image reconstruction of the conductivity distribution of a body can be calculated using measured voltages at the boundary. This is done by solving an inverse problem for an elliptic partial differential equation (PDE). In this work, we present some sensitivity results arising from the solution of the PDE. We use these to show that a segmentation approach to the EIT inverse problem has a unique solution in a suitable space using a fixed point theorem.

Submitted October 23, 2019. Published September 16, 2020.
Math Subject Classifications: 35J20, 47H10, 35R30.
Key Words: Electrical impedance tomography problem; two-phase segmentation algorithm; fixed point theorem.
DOI: 10.58997/ejde.2020.93

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Renier Mendoza
Institute of Mathematics
University of the Philippines
Diliman, Quezon City, Philippines
email: rmendoza@math.upd.edu.ph
Stephen Keeling
Institute for Mathematics and Scientific Computing
Karl-Franzens University of Graz, Austria
email: stephen.keeling@uni-graz.at

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