# Detecting stochastic inclusions in electrical impedance tomography

## TL;DR

This paper investigates detecting stochastic inclusions in electrical impedance tomography using the Factorization and Monotonicity Methods on mean Neumann-to-Dirichlet maps, demonstrating effectiveness with high-contrast anomalies through theoretical and numerical analysis.

## Contribution

It extends existing methods to stochastic conductivities, showing that anomalies can be identified via mean maps under high contrast conditions.

## Key findings

- Successful detection of stochastic inclusions using mean Neumann-to-Dirichlet maps.
- Theoretical validation of methods for high-contrast anomalies.
- Numerical examples in 2D confirm the approach's effectiveness.

## Abstract

This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the Factorization Method or the Monotonicity Method to the mean value of the corresponding Neumann-to-Dirichlet map provided that the anomaly has high enough contrast in the sense of expectation. The theoretical results are complemented by numerical examples in two spatial dimensions.