The factorization method for cracks in electrical impedance tomography

The inverse problem we are dealing with is to recover the inclusion of cracks in electrical impedance tomography from boundary measurements of current and voltage. Both the cases of Neumann and impedance boundary conditions posed on the cracks are considered. Assuming the anisotropic background conductivity is known a priori, we prove the factorization method can be applied to reconstruct the shape and location of the cracks. The numerical examples are shown to illustrate the correctness and effectiveness of the proposed method. This work is an extension of the study investigated by Bruhl et al. (ESAIM Math Model Numer Anal 35:595-605, 2001) where an insulating crack embedded in homogeneously conducting object is considered.