The Electrical Impedance Tomography Problem

Abstract

In this chapter the Electrical Impedance Tomography (EIT) is adopted as model problem, which consists in finding the number, size, shape and location of a set of hidden anomalies inside a body from total or partial measurements of the electrical potential on the boundary of the body. Since the EIT problem is written in the form of an overdetermined boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the boundary measurements and the electrical potentials obtained from the model is minimized with respect to a set of ball-shaped anomalies by using the concept of topological derivatives.