Acousto-electric tomography by the convergence of Kaczamrz two-point gradient-$\mathrm{\Theta }$ method

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-$\mathrm{\Theta }$ (TPG-$\mathrm{\Theta }$) in Kaczmarz type is proposed, with a general convex penalty term $\mathrm{\Theta }$, 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.