Abstract

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.