A unified analysis of FBP-based algorithms in helical cone-beam and circular cone- and fan-beam scans.
A unified analysis of FBP-based algorithms in helical cone-beam and circular cone- and fan-beam scans.
复制标题
对螺旋锥束、圆锥束和扇形束扫描中基于 FBP 的算法进行统一分析。
DOI：
10.1088/0031-9155/49/18/011
复制
发表时间：
2004
影响因子：
3.5
通讯作者：
Yu,Lifeng
中科院分区：
文献类型：
--
作者：
Pan,Xiaochuan;Xia,Dan;Zou,Yu;Yu,Lifeng
圆形扫描轨迹是并且可能仍然是计算机断层摄影（CT）成像中的轨迹的流行选择，因为其易于实现和控制。基于滤波反投影（FBP）的算法先前已经被开发用于在圆形锥束和扇束情况下对整个图像或图像内的感兴趣区域进行近似和精确重建。最近，我们已经开发了一种基于三维FBP的算法，用于螺旋锥束扫描中PI线段的图像重建。在这项工作中，我们证明了基于3D FBP的算法确实提供了一个相当一般的公式，从发散投影（如锥束和扇束投影）的图像重建。在此基础上，我们推导出新的近似或精确算法的图像重建在圆形锥束或扇束扫描，这可以被解释为特殊情况下的螺旋扫描。现有的算法对应的派生算法进行了鉴定。我们还进行了初步的数值研究，以验证我们的理论结果在每种情况下。所得结果可以推广到其它非圆轨迹。
A circular scanning trajectory is and will likely remain a popular choice of trajectory in computed tomography (CT) imaging because it is easy to implement and control. Filtered-backprojection (FBP)-based algorithms have been developed previously for approximate and exact reconstruction of the entire image or a region of interest within the image in circular cone-beam and fan-beam cases. Recently, we have developed a 3D FBP-based algorithm for image reconstruction on PI-line segments in a helical cone-beam scan. In this work, we demonstrated that the 3D FBP-based algorithm indeed provided a rather general formulation for image reconstruction from divergent projections (such as cone-beam and fan-beam projections). On the basis of this formulation we derived new approximate or exact algorithms for image reconstruction in circular cone-beam or fan-beam scans, which can be interpreted as special cases of the helical scan. Existing algorithms corresponding to the derived algorithms were identified. We also performed a preliminary numerical study to verify our theoretical results in each of the cases. The results in the work can readily be generalized to other non-circular trajectories.