基于单圆轨迹的Feldkamp（FDK）重建算法只有在小锥角条件下才能取得较好重建效果。随着锥角增大，图像质量迅速下降。因此在实际应用中受到一定限制。在分析了物体Radon数据与单圆扫描获得的Radon数据间的关系后，结合空间可变滤波反投影重建算法(SV_FBP)，提出了一种基于Grengeat公式的叠加算法。该重建算法由两部分重建结果叠加而成，第1部分结果首先采用FDK算法通过对单圆扫描的投影数据进行重建来获得；然后采用外推方法获得缺失的数据，并利用SV_FBP进行重建得到第2部分结果；最后将两部分结果进行叠加。实验结果表明，该算法不仅有效地抑制了FDK算法重建的伪影，而且使锥角的使用范围比FDK算法提高了３～４倍。这种新的叠加重建算法在大长物体的重建中，具有重要的理论和应用价值。

FDK algorithm based on single circular orbit can only be used when the cone angle is small. The images reconstructed by Feldkamp algorithm become blurred and distorted when the cone angle increases. As a result there is a limitation for practical application. After the relationship between the Radon transform of the object and the Radon data acquired by the scanning of the single circular orbit is analyzed in the paper and the superposing algorithm is presented based on Grengeat’s formula according to the space variant filtered backprojection(SV_FBP). The first sub result is calculated by applying the FDK algorithm to the projection data acquired by a single circular orbit scan. The second sub result is a correction received by applying SV_FBP algorithm to the missing Radon data acquired by extrapolation. The final result is the sum of the two sub results. The result demonstrates the algorithm is a valid method to reduce artifacts of the images reconstructed by FDK algorithm, and the applicable cone angle range can be 3 to 4 times larger than that of the FDK algorithm. This new superposing method will possess important theoretical and application value in the fields of big and long object reconstruction.