Hybrid Inverse Problems Arising from Acousto-Electric Coupling

Abstract

We study hybrid imaging techniques that aim to overcome the ill-posedness of the Electric Impedance Tomography using the acousto-electric coupling. For the isotropic case, we consider the problem of reconstructing the internal conductivity of an object by making electric measurements on the boundary while perturbing the conductivity by sending ultrasound waves to the object. The conductivity can be uniquely recovered by using one boundary potential. To obtain the uniqueness, the problem is reduced to an inverse problem with internal data. Lipschitz type stability results for certain internal data are also discussed. In the last part of this thesis we discuss similar inverse problems in more general settings.