In iterative reconstruction algorithms, it is very important to calculate the weighting factor quickly and accurately, which directly affects the reconstruction efficiency and accuracy of computed tomography images. In this paper, a new calculation method for accurate length weighting factor is developed. Firstly, the ray equation is determined according to the coordinates of the source and the ray's projection. Second, the intersections of the ray and the equidistant parallel planes along three coordinate axes are calculated, and the points intersecting with the reconstructed object are put into a set. Finally, when the X-axis coordinates of all points in the set are different, the points are arranged according to their X-axis coordinates; when the X-axis coordinates of all points are same, the points are arranged according to their Y-axis coordinates. The sorted point set is the intersections that the ray traverses the reconstructed object in sequence. The index and weighting factor of all voxels that the ray passes through can be determined by the sorted point set. Compared with the classical Siddon's method, it avoids the step of describing the intersections with parameters, and its calculation speed is increased by nearly 20%. The numerical simulations and real data reconstruction experiments are conducted to validate the proposed calculation method of exact length weighting factor.

中文翻译：

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锥束计算机断层扫描精确长度加权因子的新计算方法

在迭代重建算法中，快速准确地计算权重因子非常重要，直接影响计算机断层扫描图像的重建效率和精度。本文提出了一种新的精确长度加权因子的计算方法。首先，根据光源的坐标和射线的投影确定射线方程。其次，计算射线与沿三个坐标轴的等距平行平面的交点，并将与重建对象相交的点放入一个集合中。最后，当集合中所有点的X轴坐标不同时，点按其X轴坐标排列；当所有点的X轴坐标相同时，这些点根据它们的 Y 轴坐标排列。排序后的点集是光线依次穿过重构对象的交点。光线通过的所有体素的索引和权重因子可以由排序后的点集确定。与经典的Siddon方法相比，避免了用参数描述交点的步骤，计算速度提高了近20%。通过数值模拟和真实数据重建实验验证了所提出的精确长度加权因子的计算方法。与经典的Siddon方法相比，避免了用参数描述交点的步骤，计算速度提高了近20%。通过数值模拟和真实数据重建实验验证了所提出的精确长度加权因子的计算方法。与经典的Siddon方法相比，避免了用参数描述交点的步骤，计算速度提高了近20%。通过数值模拟和真实数据重建实验验证了所提出的精确长度加权因子的计算方法。