Reconstruction of conductivity distribution in electrical impedance tomography by topological derivative

Electrical impedance tomography (EIT) reconstructs the conductivity distribution of a domain using electrical data on its boundary. Shape derivatives and topological derivatives have been incorporated into level set methods to investigate shape optimization problems. The shape derivative measures the sensitivity of boundary perturbations while the topological derivative measures the sensitivity of a so-called shape functional when the domain is perturbed by small holes, inclusions, defects or cracks inside the domain. The combination of these derivatives gives an algorithm which has more flexibility in shape changing and may escape from a local optimum.