Acousto-Electric Tomography with Total Variation Regularization

We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous conductivity distributions, by reformulating it as an optimization problem with L1 fitting and total variation penalty subject to PDE constraints. We establish continuity and differentiability results for the forward map, the well-posedness of the optimization problem, and present an easy-to-implement and robust numerical method based on successive linearization, smoothing and iterative reweighing. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach.