A Factorization Scheme For Determining Conductivity Contrasts In Impedance Tomography

The inverse problem of electrical impedance tomography (EIT) is to recover the conductivity inside an investigated object from boundary measurements of current and voltage. There are a variety of methods to localize inclusions, i.e. domains in which the conductivity is different from the background conductivity such as e. g. the factorization method. However, these qualitative methods do not provide any information about the conductivity inside the inclusions. In this work, we show that factorization arguments can also be used to obtain the conductivity inside inclusions after they have been localized. This method is based on a new factorization with three operators that are different from those in the original factorization method for EIT. In particular, we investigate the spectrum of the operator that appears in the middle of this new factorization and show that it is closely related to the conductivity of the inclusions.