  We propose and test stable algorithms for the reconstruction of the internal
conductivity of a biological object using acousto-electric measurements.
Namely, the conventional impedance tomography scheme is supplemented by
scanning the object with acoustic waves that slightly perturb the conductivity
and cause the change in the electric potential measured on the boundary of the
object. These perturbations of the potential are then used as the data for the
reconstruction of the conductivity. The present method does not rely on
"perfectly focused" acoustic beams. Instead, more realistic propagating
spherical fronts are utilized, and then the measurements that would correspond
to perfect focusing are synthesized. In other words, we use \emph{synthetic
focusing}. Numerical experiments with simulated data show that our techniques
produce high quality images, both in 2D and 3D, and that they remain accurate
in the presence of high-level noise in the data. Local uniqueness and stability
for the problem also hold.
