Crawford C R, Gullberg G T, Tsui B M
Applied Science Laboratory, General Electric Company, Milwaukee, Wisconsin 53201.
Med Phys. 1988 Jan-Feb;15(1):67-71. doi: 10.1118/1.596158.
A convolutional backprojection algorithm is derived for a fan beam geometry that has an angular-dependent displacement in its center-of-rotation from the midline of the fan beam. In both x-ray computed tomography and single photon emission computed tomography, misalignment can occur when the mechanical center-of-rotation is not colinear with midline of the fan beam. In some cases the shift in the center-of-rotation is constant for every angle, whereas, in other cases it varies with angular position. 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 any 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. Simulations are performed that illustrate these artifacts and demonstrate how the new algorithm corrects for this misalignment. A method for estimating the parameters of the fan beam geometry, including the angular-dependent shift in the center-of-rotation, is also described.
推导了一种适用于扇形束几何结构的卷积反投影算法，该扇形束在其旋转中心相对于扇形束中线存在与角度相关的位移。在X射线计算机断层扫描和单光子发射计算机断层扫描中，当机械旋转中心与扇形束中线不共线时，就会出现失准情况。在某些情况下，旋转中心的偏移对于每个角度都是恒定的，而在其他情况下，它会随角度位置而变化。标准重建算法是针对旋转中心位于扇形束中线的几何结构推导出来的，这些算法直接对扇形束数据进行滤波和反投影，而无需重新组合成平行束几何结构。然而，在旋转中心存在任何失准的情况下，如果使用这些传统重建算法来重建扇形束投影，将会产生结构化伪影并导致分辨率损失。进行了模拟，展示了这些伪影，并演示了新算法如何校正这种失准。还描述了一种估计扇形束几何结构参数的方法，包括旋转中心与角度相关的偏移。
