Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type

Abstract Acousto-electric tomography (AET) is a new hybrid imaging technique. It recovers the conductivity of biological tissue using the internal power density distribution and overcomes the shortcomings of classical electrical impedance tomography (EIT), where only the boundary measurement data are applied. In this manuscript, we consider the numerical realization of the AET model. Inspired by the work [18], we develop an adaptive Nesterov method of Kaczmarz type. The combination parameters are no longer chosen by line search, but through adaptive procedures with explicit formulas, which greatly improve the computational efficiency. Furthermore, uniformly convex regularization functionals are incorporated to reconstruct the conductivity with sparsity or discontinuity. The convergence property of the method is rigorously proven under reasonable conditions. Numerical simulations are presented to illustrate the efficiency and feasibility of our proposed method. We emphasize that the proposed method is also applicable for other nonlinear inverse problems with multiple operators.