  We study the numerical reconstruction problem in acousto-electric tomography
(AET) of recovering the conductivity distribution in a bounded domain from
multiple interior power density data. The Two-Point-Gradient-$\Theta$
(TPG-$\Theta$) in Kaczmarz type is proposed, with a general convex penalty term
$\Theta$, the algorithm can be utilized in AET problem for recovering sparse
and discontinuous conductivity distributions. We establish the convergence of
such iterative regularized method. Extensive numerical experiments are
presented to illustrate the feasibility and effectiveness of the proposed
approach.
