A Complete Reconstruction Procedure for Acousto-Electric Tomography with Unknown Noise Level

Acousto-electric tomography (AET) is a hybrid imaging modality. It improves the spatial resolution of conductivity imaging by combining acoustic and electrical measurements. The AET inverse problem involves two steps. First, the interior power density is reconstructed from acoustically perturbed boundary measurements. Second, the conductivity distribution is recovered based on the reconstructed power density. Most existing studies focus on the second step and assume that the noise level is known. In this work, we examine the complete AET reconstruction procedure in a realistic scenario where the noise levels are unknown. The power density is reconstructed from a linearized Fredholm integral equa tion of the first kind, using Tikhonov regularization, with the regularization parameter chosen by the heuristic Hanke–Raus rule. The conductivity is then recovered by a nonlinear Landweber–Kaczmarz it eration arising from multiple boundary current injections. Rigorous convergence analysis is established under the heuristic stopping criterion, representing the first theoretical study of an AET reconstruction method combined with a heuristic stopping rule. Numerical experiments are carried out under two different sound-speed settings, namely, a fixed sound speed and a perturbed sound speed derived from a numerical breast tissue model. The results demonstrate the effectiveness of the proposed approach, including its ability to accurately reconstruct nonsmooth conductivities.