The factorization method for EIT in the case of mixed inclusions

The inverse problem of electrical impedance tomography (EIT) is to recover the conductivity inside an investigated subject from boundary measurements of current and voltage. In this work, we deal with the simpler case in which the background conductivity is known a priori and we wish to locate inclusions, i.e. domains inside the investigated subject having a different conductivity than the background. A very successful method for solving this problem is the factorization method. However, for the factorization method in EIT it is usually assumed that there is only one type of inclusions present, e.g. only inclusions with a higher or with a lower conductivity than the background. The question of whether the factorization method also works in the mixed case is still an open problem. Here we present a modified version of the method to cope with this case that makes use of some a priori information about where the inclusions are roughly located. We show that under this assumption we can even detect inclusions in the mixed case.