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 L ¹ fitting and total variation penalty subject to PDE constraints. We establish continuity and differentiability results for the forward map, and the well-posedness of the optimization problem, and present an easy-to-implement and robust numerical method based on successive linearization, smoothing and iterative reweighting. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach. (paper)