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.

翻译：针对Riemannian辐射传输方程（RRTE）的系数反问题（CIP），本文首次构建了全局收敛的数值方法。该方法属于该研究团队针对其他偏微分方程（PDE）的系数反问题多年来持续研究的"凸化"方法变体。这些偏微分方程与RRTE存在显著差异。数值方案中Carleman权函数（CWF）的存在是确保全局收敛的关键要素。本文给出了收敛性分析及数值实验结果，验证了理论结论。RRTE描述了光子在不均匀介质中沿测地线传播的输运过程，其测地线由介质空间变化的介电常数决定。