A Cone-beam CT Reconstruction Algorithm Based on Grangeat''''s Formula
一种基于Grengeat公式的锥束CT重建算法研究

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.