圆弧加直线轨迹Katsevich类型的锥束CT重建算法

由于圆与直线轨迹的交点处存在轨迹变量的偏导数,Katsevich算法直接忽略了关于构造因子的分析,从而对后续重建计算产生影响,导致重建结果出现伪像。通过对该问题进行研究,确定轨迹交点处的构造因子,并推导出在平板检测器下与两段轨迹相对应的重建公式。据此引申出一个不含有关于轨迹变量偏导的等价公式,从而计算出轨迹交点处相应的重建贡献值。同时,提出使用光滑过渡函数改善因反投影区域边界的不连续性而对重建结果产生的影响。利用Forbild头模型进行仿真模拟,实验结果表明,改进的算法有效地抑制了重建结果的伪像。

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.