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走时层析成像是根据首波走时重建声波、地震波或电磁波波速的层析技术，其所用到的射线路径依赖于波速分布．本文提出了一个依据费马原理寻找射线路径的新方法．费马原理指出，从发射点到接点的射线首波的走时极小，因此寻找射线路径的问题是一个最优化问题。我们用加权有向图中寻找最短路经的思想来解决，然后将所得到的射线路径用于一个迭代重建算法中．模拟结果证明该重建算法优于传统的算法，并且稳定性很好．
Time-of-flight tomography is a tomography technique that reconstructs acoustic, seismic, or electromagnetic wave velocities based on the travel time of the first wave, and the ray paths used depend on the velocity distribution. In this paper, we propose a new method to find ray paths based on Fermat’s principle. Fermat’s principle points out that the travel time of the first wave from the launch point to the contact point is extremely small, so finding the ray path is an optimization problem. We use the weighted digraph to find the shortest path to solve the idea, and then use the resulting ray path for an iterative reconstruction algorithm. Simulation results show that the reconstruction algorithm outperforms the traditional one and has good stability.