为提高扇束滤波反投影(FBP)算法重建CT图像的速度, 提出了利用正余弦函数性质对极坐标反投影算法进行优化的快速重建方法。首先将扇束等距CT扫描得到的投影数据进行加权, 卷积滤波处理; 其次将预处理后的投影数据运用正余弦函数性质进行极坐标反投影重建。试验结果表明, 与传统的卷积反投影重建算法相比, 该方法可以将重建速度提高4倍以上, 而且重建质量与传统卷积反投影相当。这种算法也适应于多层螺旋三维重建, 并且可以推广到三维锥束重建。

To improve the reconstruction speed of CT image reconstruction based on fan-beam filtered back-projection(FBP), this paper proposes a fast reconstruction method for the back-projection algorithm of the polar coordinates based on the features of sine and cosine function. The projection data from CT scanning of the fan-beam with equidistant detectors are firstly weighted and convolution filtered, and secondly the preprocessing projection data are back-projected on the polar coordinates reconstruction grid using the features of sine and cosine function. The experimental results showed that, compared with the traditional convolution back-projection algorithm, this method could improve the speed by more than 4 times, and the reconstruction quality was as good as that of the traditional convolution back-projection. The algorithm can also be applied to multi-slice helical 3D cone-beam reconstruction.