# Numerical determination of anomalies in multifrequency electrical impedance tomography

## TL;DR

This paper introduces a spectral decomposition method for detecting anomalies in multifrequency electrical impedance tomography, enabling the reconstruction of conductivity profiles with high accuracy using gradient descent algorithms.

## Contribution

It presents a novel spectral decomposition approach to identify and reconstruct anomalies in multifrequency electrical impedance tomography, improving detection accuracy.

## Key findings

- Successful reconstruction of anomalies using spectral decomposition.
- Effective use of gradient descent for numerical experiments.
- Enhanced detection of piecewise constant conductivities.

## Abstract

The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the conductivity distribution is piecewise constant, takes a constant value outside a single smooth anomaly, and a frequency dependent function inside the anomaly itself. Using an original spectral decomposition of the solution of the forward conductivity problem in terms of Poincar\'e variational eigenelements, we retrieve the Cauchy data corresponding to the extreme case of a perfect conductor, and the conductivity profile. We then reconstruct the anomaly from the Cauchy data. The numerical experiments are conducted using gradient descent optimization algorithms.