基于转角增量关系的FDK锥束重建改进算法

单圆形轨迹不能满足锥束投影精确重建的充要条件是经典FDK算法出现锥向衰减伪像的根本原因.通过斜平面转角增量关系的分析,推导出同锥角斜平面间转角及其增量的计算关系,进而得出FDK算法是对同锥角斜平面族上有限视角的投影数据进行重建,并且在滤波反投影重建过程中存在转角关系不匹配问题.针对上述两个问题,提出了一种利用转角及其增量关系对FDK算法进行改进的新方法,改进思路也进一步推广到T-FDK算法中.Shepp-Logan模型的仿真实验结果表明在适中或较大锥角情况下,改进算法显著改善了FDK算法所存在的锥向衰减伪像.

Modified FDK cone-beam reconstruction algorithm based on relationship of rotation angle increment

Due to the incomplete data set for exact conerbeam reconstruction with a circular scan trajectory, the FDK algorithm produces artifact of the intensity drop with increasing cone angle. First, the relationship of the rotation angle increments in the tilted plane was investigated. And then, the value of the rotation angle is obtained in any family of the tilted planes which has the same cone angle relative to the midplane. As a result, there are two important details ignored by the classical FDK algorithm. One is the limited-angle projection data acquired in a family of the tilted planes. The other is the difference of rotation angle between the midplane and the tilted plane at the same projection angle. Therefore, based on these two aspects, a modified method is proposed for the FDK algorithm using the relationship of the rotation angle increment. Also, the same idea is applied to the T-FDK algorithm. Computer-simulated studies show that the proposed algorithms effectively reduce the artifact of the intensity drop inherent to the FDK algorithm at appropriate or big cone angle.