Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
Phys Med Biol. 2013 Mar 7;58(5):1415-31. doi: 10.1088/0031-9155/58/5/1415. Epub 2013 Feb 11.
We introduce a fast algorithm to backproject fan-beam tomographic projections. For typical configurations of computed tomography scanners, the algorithm reduces the number of computations and actual runtimes by an order of magnitude. Similar to fast algorithms for the parallel-beam geometry, this algorithm is a divide-and-conquer method that aggregates the projections in a hierarchical manner. The computational speedup results from the use of sparse sampling grids to represent images that are comprised of a small number of projections that are close together in view-angle. In the parallel beam case these sparse (Cartesian) sampling grids were constructed by exploiting the projection slice theorem. Extending the parallel beam algorithms to fan-beam is a significant step because there is no equivalent to the projection-slice theorem for the fan-beam geometry. This was achieved using a novel analysis of fan-beam backprojection that characterizes the spatially-varying frequency content. This analysis, which we present here, allows for the construction and use of the sparse (non-Cartesian) sampling grids.
我们介绍了一种用于扇形束层析投影反投影的快速算法。对于计算机断层扫描扫描仪的典型配置，该算法将计算量和实际运行时间减少了一个数量级。与平行束几何形状的快速算法类似，该算法是一种分治方法，以层次方式聚合投影。计算速度的提高来自于使用稀疏采样网格来表示图像，这些图像由视图角度上彼此接近的少量投影组成。在平行束情况下，这些稀疏（笛卡尔）采样网格是通过利用投影切片定理来构建的。将平行束算法扩展到扇形束是一个重要的步骤，因为扇形束几何形状没有等效的投影切片定理。这是通过对扇形束反投影的新颖分析来实现的，该分析描述了空间变化的频率内容。我们在这里介绍的这种分析允许构建和使用稀疏（非笛卡尔）采样网格。
