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.

翻译：我们研究了声电断层成像（AET）中的数值重建问题，即从多个内部功率密度数据中恢复有界域内的电导率分布。提出了一种Kaczmarz类型的两点梯度-Θ（TPG-Θ）方法，其中包含一般凸罚项Θ，该算法可用于AET问题中恢复稀疏且不连续的电导率分布。我们建立了这种迭代正则化方法的收敛性。通过大量数值实验验证了所提方法的可行性与有效性。