IEEE Trans Med Imaging. 1986;5(1):23-9. doi: 10.1109/TMI.1986.4307735.
A convolutional backprojection algorithm is derived for a fan beam geometry that has its center-of-rotation displaced from the midline of the fan beam. In single photon emission computed tomography (SPECT), where a transaxial converging collimator is used with a rotating gamma camera, it is difficult to precisely align the collimator so that the mechanical center-of-rotation is colinear with the midline of the fan beam. A displacement of the center-of-rotation can also occur in X-ray CT when the X-ray source is mispositioned. Standard reconstruction algorithms which directly filter and backproject the fan beam data without rebinning into parallel beam geometry have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of a misalignment of the center-of-rotation, if these conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. We illustrate these artifacts with simulations and demonstrate how the news algorithm corrects for this misalignment. We also show a method to estimate the parameters of the fan beam geometry including the shift in the center-of-rotation.
推导出了一种扇束几何的卷积反向投影算法，其中旋转中心从扇束的中线偏移。在单光子发射计算机断层扫描（SPECT）中，使用具有旋转γ相机的横向会聚准直器，很难精确对准准直器，使得机械旋转中心与扇束的中线共线。当 X 射线源错位时，在 X 射线 CT 中也会发生旋转中心的位移。已经为其旋转中心位于扇束中线的几何形状推导出了直接对扇束数据进行滤波和反向投影而无需重新-bin 到平行束几何形状的标准重建算法。然而，在旋转中心不对准的情况下，如果使用这些传统的重建算法来重建扇束投影，则会产生结构伪影和分辨率的损失。我们用模拟来说明这些伪影，并演示新算法如何纠正这种不对准。我们还展示了一种估计扇束几何形状参数的方法，包括旋转中心的偏移。
