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In iterative reconstruction algorithms, it is very important to calculate the weighting factor quickly and accurately, which directly affects the reconstruction efficiency and accuracy of computed tomography images. In this paper, a new calculation method for accurate length weighting factor is developed. Firstly, the ray equation is determined according to the coordinates of the source and the ray's projection. Second, the intersections of the ray and the equidistant parallel planes along three coordinate axes are calculated, and the points intersecting with the reconstructed object are put into a set. Finally, when the X‐axis coordinates of all points in the set are different, the points are arranged according to their X‐axis coordinates; when the X‐axis coordinates of all points are same, the points are arranged according to their Y‐axis coordinates. The sorted point set is the intersections that the ray traverses the reconstructed object in sequence. The index and weighting factor of all voxels that the ray passes through can be determined by the sorted point set. Compared with the classical Siddon's method, it avoids the step of describing the intersections with parameters, and its calculation speed is increased by nearly 20%. The numerical simulations and real data reconstruction experiments are conducted to validate the proposed calculation method of exact length weighting factor. [ABSTRACT FROM AUTHOR]

In computed tomography (CT) image reconstruction, the iterative algorithms have many advantages that the analytic algorithms don't have. However, the calculation of system matrix is time-consuming, which affects their application in real-time CT image reconstruction. In this paper, a fast system matrix calculation method is proposed on the basis of that the distance between the voxel and the adjacent rays reflects the contribution of the voxel to the ray projections. Firstly, every voxel is projected at a projection angle, and then the weighting factor is determined according to the distance between the voxel's projection and the adjacent ray projection on the detector. Finally, the ray equations and weighting factors corresponding to every voxel at all projection angles are obtained. The calculation amount of the proposed method are greatly improved compared with the current grid traversal (GT) method, and it has good parallel computing performance. In the simulation experiment, the Shepp-Logan head phantom is reconstructed by using the proposed system matrix calculation method and algebraic reconstruction technique (ART). Compared with GT method, its cost is reduced by nearly 30 %, and its acceleration ratio is four times that of the GT method. The experimental results show that it is a fast and effective method to calculate the system matrix. [ABSTRACT FROM AUTHOR]