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arXiv · 1812.05300

Monotonicity based shape reconstruction in electrical impedance tomography

Bastian Harrach·Marcel Ullrich
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Abstract

Current-voltage measurements in electrical impedance tomography can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators (NtD). With this ordering, a point-wise larger conductivity leads to smaller current-voltage measurements, and smaller conductivities lead to larger measurements. We present a converse of this simple monotonicity relation and use it to solve the shape reconstruction (aka inclusion detection) problem in EIT. The outer shape of a region where the conductivity differs from a known background conductivity can be found by simply comparing the measurements to that of smaller or larger test regions.

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Bastian Harrach, Marcel Ullrich. 2018-12-13. Monotonicity based shape reconstruction in electrical impedance tomography. https://doi.org/10.1137/120886984

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