  In acousto-electric tomography the goal is to reconstruct the electric
conductivity in a domain from electrostatic boundary measurements of
corresponding currents and voltages, while the domain is penetrated by a
time-dependent acoustic wave. We explicitly model the phenomena, and we propose
a complete inversion framework for acousto-electric tomography in two steps:
First the interior power density is obtained from boundary measurements by
solving a linear, ill-posed problem; second the interior conductivity is
reconstructed from the power density by solving a non-linear, fairly well-posed
problem. We perform numerical experiments on synthetic data with realistically
chosen parameters. We investigate how feasibility of reconstructing the
electrical conductivity from boundary measurements depends on the
acousto-electric coupling constant and measurement noise. Our findings are
positive, and indicate that AET is indeed feasible for interesting applications
in for example medical imaging. Finally, we consider a limited angle setup and
show that the conductivity is well reconstructed near the measurement boundary.
