The factorization method for three dimensional electrical impedance tomography

The use of the factorization method for electrical impedance tomography has been proved to be very promising for applications in the case where one wants to find inhomogeneous inclusions in a known background. In many situations, the inspected domain is three dimensional and is made of various materials. In this case, the main challenge in applying the factorization method is in computing the Neumann Green's function of the background medium. We explain how we solve this difficulty and demonstrate the capability of the factorization method to locate inclusions in realistic inhomogeneous three dimensional background media from simulated data obtained by solving the so-called complete electrode model. We also perform a numerical study of the stability of the factorization method with respect to various modelling errors.