Implementation of the low-discrepancy spherical trajectory and visualization in Matlab from Selection and evaluation of spherical acquisition trajectories for industrial computed tomography

In conventional industrial computed tomography, the source–detector system rotates in equiangular steps in-plane relative to the part of investigation. While being by far the most frequently used acquisition trajectory today, this method has several drawbacks like the formation of cone beam artefacts or limited usability in case of geometrical restrictions. In such cases, the usage of alternative spherical trajectories can be beneficial to improve image quality and defect visibility. While investigations have been performed to relate the influence of the trajectory choice in the typical metrological case of a high number of available projections, so far barely any work has been done for the case of few source–detector poses, which is more relevant in the field of non-destructive testing. In this work, we provide an overview of quantitative metrics that can be used to assess the image quality of reconstructed CT volumes, discuss their advantages and drawbacks and propose a framework to investigate the performance of several non-standard trajectories with respect to previously defined regions of interest. Inspired by pseudorandom sampling methods for Monte–Carlo-algorithms, we also suggest an entirely new trajectory design, the low-discrepancy spherical trajectory, which extends the concept of equiangular planar trajectories into three dimensions and can be used for benchmarking and comparison to other spherical trajectories. Last, we use an optimization method to calculate task-specific acquisition trajectories and relate their performance to other spherical designs.在常规工业计算机断层扫描（Computed Tomography，CT）中，源-探测器系统相对于被检测工件沿平面内以等角步长进行旋转。尽管该方法是目前应用最广泛的采集轨迹，但存在诸多缺陷，例如锥束伪影的产生，以及在存在几何限制的场景下可用性受限。在此类场景下，采用替代球面轨迹可有效提升图像质量与缺陷可视性。尽管已有研究针对可用投影数量充足的典型计量场景，分析了轨迹选择带来的影响，但针对源-探测器位姿数量较少的场景的相关研究却极少，而该场景在无损检测领域更具实际意义。本研究综述了可用于评估重建CT体数据图像质量的定量指标，探讨了各类指标的优劣，并提出了一个研究框架，用于针对预先定义的感兴趣区域（Regions of Interest，ROI）分析多种非标准轨迹的性能表现。受蒙特卡洛算法伪随机采样方法的启发，本研究还提出了一种全新的轨迹设计方案——低偏差球面轨迹，该方案将等角平面轨迹的概念拓展至三维空间，可用于基准测试以及与其他球面轨迹进行对比。最后，本研究采用优化方法计算任务专属采集轨迹，并将其性能与其他球面轨迹设计方案进行关联对比。