2D and 3D reconstructions in acousto-electric tomography via two-point gradient Kaczmarz-type algorithm

Abstract

This paper presents a Kaczmarz type two-point gradient algorithm with the general convex penalty functional $\Theta$ (KTPG-$\Theta$), for efficient reconstruction of conductivity in acousto-electric tomography (AET). The algorithm optimizes a convex functional with flexible non-smooth regularization terms, such as $L^1$-like and total variation-like, to handle sparse and discontinuous conductivity distributions. By cyclically processing the measurement equations and incorporating an acceleration strategy, the proposed method achieves high computational efficiency while ensuring convergence. Numerical experiments on both synthetic and realistic phantoms demonstrate the method’s superior accuracy, strong noise robustness, and ability to resolve fine details. Beyond AET, the KTPG-$\Theta$ framework can be applied to a wide range of nonlinear inverse problems involving systems of equations, showcasing its potential for broader applications in science and engineering.