# Monotonicity based shape reconstruction in electrical impedance tomography

## TL;DR

This paper introduces a monotonicity-based method for shape reconstruction in electrical impedance tomography, enabling the detection of inclusions by comparing measurements with test regions, based on a novel converse relation.

## Contribution

It presents a new converse monotonicity relation in EIT that simplifies shape reconstruction by direct comparison of measurements with test regions.

## Key findings

- Effective inclusion detection using monotonicity comparisons.
- The method provides a straightforward approach to shape reconstruction.
- The approach is based on a novel monotonicity relation in the NtD operators.

## 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.