Abstract. The Katsevich algorithm is a breakthrough in the theoretically exact algorithms for helical cone beam computed tomography (CT). For future application in medical and industrial CT, determining how to implement it efficiently and accurately is the main task. We analyzed the slope law and intersection law of the k-lines, finding that the k-lines are not intersecting if the half-maximal fan angle (HMFA) is <21 deg (numerical solution, so it is approximate) and that the helical pitch and HMFA determine the depth of parallelism of k-lines. Using an appropriate pitch and an HMFA that is <21 deg, one can use a simplified Katsevich algorithm, whose filtration process can be done on the rows of the detector panel so that the preweighting, pre-rebinning, post-rebinning, and postweighting steps are all canceled. Simulation experiments show that the simplified algorithm can obtain highly precise images at a faster speed. Our results are intended to be valuable to those who are working on efficient implementations of the Katsevich-type algorithms.

中文翻译：

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受 k 线分布特性启发的简化 Katsevich 算法

摘要。Katsevich 算法是螺旋锥束计算机断层扫描 (CT) 理论上精确算法的突破。对于未来在医疗和工业CT中的应用，确定如何高效、准确地实施是主要任务。我们分析了 k 线的斜率定律和相交定律，发现如果半最大扇形角 (HMFA) 小于 21 度（数值解，所以它是近似的），则 k 线不相交，并且螺旋节距和 HMFA 决定了 k 线的平行深度。使用适当的间距和 <21 度的 HMFA，可以使用简化的 Katsevich 算法，其过滤过程可以在检测器面板的行上完成，以便预加权、预重组、后重组和后加权步骤都取消了。仿真实验表明，该简化算法能够以更快的速度获得高精度的图像。我们的结果旨在对那些致力于高效实现 Katsevich 型算法的人有价值。