# EIT reconstruction using virtual X-rays and machine learning

RNTW02 - Rich and non-linear tomography in medical imaging, materials and non destructive testing

The mathematical model of electrical impedance tomography (EIT) is the inverse conductivity problem introduced by Calder\’on. The aim is to recover the conductivity $\sigma$ from the knowledge of the Dirichlet-to-Neumann map $\Lambda_\sigma$. It is a nonlinear and ill-posed inverse problem. We introduce a new reconstruction algorithm for EIT , which provides a connection between EIT and traditional X-ray tomography. We divide the exponentially ill-posed and nonlinear inverse problem of EIT into separate steps. We start by mathematically calculating so-called virtual X-ray projection data from the DN map. Then, we perform explicit algebraic operations and one-dimensional integration, ending up with a blurry Radon sinogram. We use neural networks to deconvolve the sinogram and finally, we can compute a reconstruction of the conductivity using the inverse Radon transform. We demonstrate the method with simulated data examples.   This is a joint work with Samuli Siltanen, Matti Lassas, Rashmi Murthy, Fernando Silva de Moura, Juan Pablo Agnelli, and Melody Alsaker.

This talk is part of the Isaac Newton Institute Seminar Series series.