Cone-Beam CT Reconstruction of Katsevich-Type Algorithm for Orthogonal Arc-and-Line Trajectory

Because Katsevich algorithm includes the partial derivative with respect to the variable of trajectory, the analysis of structure factor and subsequent computation of reconstruction are ignored at the intersection point of two source orbits consisting of a circle and orthogonal lines, which may induce artifacts in the reconstructed image. This paper investigates the Katsevich algorithm for this geometry, determines the structure factor at the intersection point, and deduces the corresponding reconstruction formula about two source trajectories using the planar detector. As a result, an equivalence formula is achieved excluding the partial derivative with respect to the variable of trajectory and can be used to calculate the contribution of critical plane at the intersection point. In addition, a smooth transitional function is suggested to improve the discontinuity of contribution at the border of projection region defined by PI-lines. Computer simulations about Forbild phantom show a reduction of the artifacts that are found with the Katsevich algorithm and verify the validity of the proposed algorithm.