Katsevich-type cone-beam CT reconstruction for single circular arc trajectory

A shift-invariant filtered backprojection cone-beam reconstruction algorithm is presented based on the Katsevich′s general inverse formula,and validated for the single circular arc trajectory.The geometrical position between trajectory plane and Radon plane rotating around the projection direction is analysed,and the stipulation for the normal vector of Radon plane is described according to the arrangement of projection data in the memory.Based on that,the detector plane is divided into six sub regions,and then the distribution of the structure factor is investigated to be relevant to arc ends.In order to obtain better reconstruction,two corresponding formulas are derived which satifies the sampling requirements of projection rate along filtering line.Computer simulations about Forbild phantom show a reduction of the artifacts that are found with the FDK-type algorithm and the validity for reconstruction of the long object.