基于移动激光气体遥测技术获取气体浓度二维分布主要通过图像重建算法实现，其中快速计算投影系数是图像重建的关键，然而基于移动激光气体遥测技术的遥测起点会随机分布在重建区域的网格内或网格线上，现有的快速投影系数递推计算方法均不适用。针对此问题，提出一种无起点约束的快速投影系数递推计算方法，设计3个光程累积因子，在不增加计算量的前提下，统一了遥测起点在网格内和网格线上的递推过程，实现了无起点约束的投影系数的快速计算。利用代数重建技术进行重建实验，结果表明，相对均方根误差最小约为0.113%，计算速度最高约为经典Siddon算法的13.9倍。该递推计算方法应用范围更广，且实现了无起点约束的投影系数递推计算。
The two-dimensional gas concentration distribution obtained based on mobile laser gas telemetry technology is mainly achieved through an image reconstruction algorithm. Fast calculation of the projection coefficient is the key for such algorithm. However, the telemetry starting point based on mobile laser gas telemetry technology is randomly distributed in the grid or on the grid line of the reconstruction area, and the existing fast recursive calculation methods of projection coefficient are not applicable. This paper proposes a fast recursive calculation method of projection coefficient without starting point constraint. Three optical path accumulation factors are designed, which unify the recursive process of telemetry starting point in the grid and on the grid line without increasing the amount of calculation and realize the fast calculation of projection coefficient without starting point constraint. Algebraic reconstruction technology is used for reconstruction experiments, which verifies the effectiveness of this method. The minimum relative root mean square error is about 0.113%, and the maximum calculation speed is about 13.9 times that of the classical Siddon algorithm. The recursive calculation method proposed in this paper has a wider range of applications. It is the first time to realize the recursive calculation of projection coefficients without starting point constraints.
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