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" principle, 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 RRTE. The presence of the Carleman Weight Function (CWF) in the
numerical scheme is the key element of the convexification. CWF is the
function, which is involved as the weight function in the Carleman estimate for
the corresponding PDE operator. 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