| Abstract: |
| In this work, we address the inverse problem of radiative transfer equation (RTE) using the Random Ordinate Method (ROM) for the forward problem and the Stochastic Gradient Descent (SGD) based method for the inverse problem, aimed at efficiently reconstructing the absorption and scattering coefficients by minimizing the mismatch between computed and measured outgoing data. Since the Discrete Ordinates Method (DOM) for solving RTE is computationally intensive and suffers from the ray effect, we utilize ROM to mitigate the ray effect due to the low regularity of the solution in the velocity direction. ROM offers several advantages over DOM, including comparable computational costs, minimal changes to existing code, and ease of parallelization. The SGD algorithm requires low memory and computation, and advances fast. Numerical examples demonstrate the accuracy and efficiency of the proposed method |
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