In this paper, we introduce a new class of projectors for 3D cone beam tomographic reconstruction. We find analytical formulas for the relationship between the voxel volume projected onto a given detector pixel and its contribution to the extinction value detected on that pixel. Using this approach, we construct a near-exact projector and backprojector that can be used especially for algebraic reconstruction techniques. We have implemented this cutting voxel projector and a less accurate, speed-optimized version of it together with two established projectors, a ray tracing projector based on Siddon's algorithm and a TT footprint projector. We show that the cutting voxel projector achieves, especially for large cone beam angles, noticeably higher accuracy than the TT projector. Moreover, our implementation of the relaxed version of the cutting voxel projector is significantly faster than current footprint projector implementations. We further show that Siddon's algorithm with comparable accuracy would be much slower than the cutting voxel projector. All algorithms are implemented within an open source framework for algebraic reconstruction in OpenCL 1.2 and C++ and are optimized for GPU computation. They are published as open-source software under the GNU GPL 3 license, see https://github.com/kulvait/KCT_cbct.
翻译:在本文中, 我们为 3D 锥形光束图的重建引入了一个新的投影器类别 。 我们找到一个分析公式, 分析投射到给定探测器像素的 voxel 体积及其对于该像素所检测的灭绝值的贡献之间的关系。 使用这个方法, 我们建造了一个近操作投影仪和背投影仪, 特别是用于变形重建技术。 我们实施了这个切除 voxel 投影仪, 并且与两个已经建立的投影机一起, 一种不那么精确的、 速度优化的投影机, 一个基于Siddon 算法的射线追踪投影仪和一个TT脚印投影投影仪。 我们显示, 切除 voxel 投影机在一个开放源框架内取得了效果, 特别是大锥形光束角度, 其精度明显高于 TTT 投影仪。 此外, 我们实施的剪切 voxel 投影机的宽松版本比当前测影仪的安装速度要快得多。 我们进一步显示, Sidddon的精确度比切投影投影机的算法要慢得多得多。 。 所有算法都在开放源框架内, GPLBLBSlevaxleval 和GDLSlals 的GlevalSlevals 正在 的软 的软的GSlevalsxxxxxxxxxxxxxxlmal