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Inverse source problem of radiative transfer: a special case of the attenuated Radon transform

The inverse source problem for the radiative transfer equation (RTE) is considered. It is shown that the stationary RTE can be obtained using an elliptic integral-differential Dyson equation as its geometric optics approximation. The explicit asymptotic expansion for solution of the Dyson equation is obtained, which leads to a formula for the asymptotic solution of the inverse problem.