基于等距扇形束滤波反投影(FBP)算法推导了一种新的算法求导希尔伯特反投影(DHB)算法，研究了DHB算法在频域对投影的滤波特性。通过理论分析和实验验证，指出由于DHB滤波函数在高频段对于锐截止特性的改善，很大程度上消除了重建图像的抖动现象。并且算法中去掉了反投影算子中的距离加权运算，使计算速度进一步提高。

A derivation Hilbert backprojection (DHB) reconstruction algorithm based on the filtered backprojection (FBP) algorithm in equispaced fan-beam CT is proposed and realized. Because of the improvement of sharp cut-off characteristic of DHB filtering function in high frequency, the experimental result shows that the reconstructed image using DHB is smoother than that using FBP. Simultaneously, the distance weighting in backprojection operator is got rid of, which leads to the reduction in reconstruction time.