  The first globally convergent numerical method for a Coefficient Inverse
Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is
constructed. This is a version of the so-called \textquotedblleft
convexification" method, which has been pursued by this research group for a
number of years for some other CIPs for PDEs. Those PDEs are significantly
different from the RRTE. The presence of the Carleman Weight Function (CWF) in
the numerical scheme is the key element which insures the global convergence.
Convergence analysis is presented along with the results of numerical
experiments, which confirm the theory. RRTE governs the propagation of photons
in the diffuse medium in the case when they propagate along geodesic lines
between their collisions. Geodesic lines are generated by the spatially
variable dielectric constant of the medium.
