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We propose a data-assisted two-stage method for solving an inverse randomsource problem of the Helmholtz equation. In the first stage, the regularizedKaczmarz method is employed to generate initial approximations of the mean andvariance based on the mild solution of the stochastic Helmholtz equation. Adataset is then obtained by sampling the approximate and corresponding trueprofiles from a certain a-priori criterion. The second stage is formulated asan image-to-image translation problem, and several data-assisted approaches areutilized to handle the dataset and obtain enhanced reconstructions. Numericalexperiments demonstrate that the data-assisted two-stage method providessatisfactory reconstruction for both homogeneous and inhomogeneous media withfewer realizations.

A data-assisted two-stage method for the inverse random source problem