%I Institute of Physics %N 3 %J Inverse Problems %K acousto-electric tomography, reconstruction, total variation %L discovery10059459 %V 35 %T Acousto-Electric Tomography with Total Variation Regularization %D 2019 %O This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. %A B Adesokan %A B Jensen %A B Jin %A K Knudsen %X 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, 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.