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：本文构建了第一种全局收敛的数值方法来求解黎曼辐射传输方程（RRTE）的系数反问题（CIP）。这是一种凸优化方法的版本，研究小组多年来一直在研究其他PDE的一些CIP。RRTE和这些PDE有显著的不同之处。这个数值方案中的CWF是保证全局收敛的关键元素。本文提供了收敛性分析和数值实验结果，结果证明了理论的正确性。RRTE描述了光子在扩散介质中沿其碰撞位置之间的测地线传播的规律。测地线由介质的空间变化介电常数产生。