English

Monotonicity based shape reconstruction in electrical impedance tomography

Numerical Analysis 2018-12-14 v1 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.1812.05300,
  title  = {Monotonicity based shape reconstruction in electrical impedance tomography},
  author = {Bastian Harrach and Marcel Ullrich},
  journal= {arXiv preprint arXiv:1812.05300},
  year   = {2018}
}
R2 v1 2026-06-23T06:41:07.969Z