Application of the factorization method to the characterization of weak inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a body from boundary measurements of current and voltage. In many practically important situations, the object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. It has been shown that the inhomogeneities can be characterized by the factorization technique if the conductivity coefficient jumps to a higher or lower value on the boundaries of the inclusions. In this paper, we extend the results to the case of weaker inclusions: If the inhomogeneities inside the body are more (or less) conductive than the known background, if the conductivity coefficient and its m−1 lowest normal derivatives are continuous over the inclusion boundaries, and if the mth normal derivative of the conductivity jumps on the inclusion boundaries, then the factorization method provides an explicit characterization of the inclusions.