基于交替投影的CT图像重建算法

目的 探讨基于交替投影的CT图像重建算法的可行性。方法 将CT图像的重建转化为凸集优化问题，将重建模型分解为多个约束，并确定其对应的凸集，通过交替投影的方式在其交集中找到可行解。对TV先验项构成的凸集的求解，通过定义TV函数的上方图集，利用点到这个凸集的切向超平面的连续投影，找到起始点到TV凸集最近的点。分别采用CPTV算法、TV-POCS算法和基于交替投影的CT图像重建算法对Shepp-Logan头部图像进行重建，比较不同算法对不同角度投影图像重建后的均方根误差（RMSE）。分别采用TV-POCS算法和基于交替投影的CT图像重建算法对小鼠脊椎轴位图像进行重建，比较两种算法的归一化均方距离（d）和归一化平均绝对距离（r）。结果 CPTV算法所重建的图像平滑性较差，伪影较多，而TV-POCS算法和基于交替投影的重建算法不仅有效抑制了噪声，还保护了图像的边缘，图像质量较高。基于交替投影的重建算法的RMSE比另外两种算法下降速度更快，收敛值更小。基于交替投影的重建算法重建图像的d和r值均小于TV-POCS算法（0.064 0 vs 0.262 4，0.073 7 vs 0.298 2）。结论 采用基于交替投影的重建算法重建有限角度的CT投影图像不需参数估计，且图像质量更高，收敛速度更快。

CT image reconstruction algorithm based on alternative projection

Objective To explore the feasibility of CT image reconstruction algorithm based on alternative projection.Methods A convex set optimization problem changed CT image reconstruction, which decomposed reconstruction model into multiple restraints and determined the corresponding convex sets. Alternative projection was used to find the solution in the intersection of the convex sets. To solve the convex set constructed by total variation (TV) prior constrains, epigraph set of the TV function was defined, and continuous projection of point to the tangential hyper-planes of the epigraph set was used to find the nearest point of the start point to the TV convex set. Chambolle-Pock for TV minimization (CPTV), TV projection onto convex set (TV-POCS) and the reconstruction algorithm based on alternative projection were used to reconstruct Shepp-Logan head image respectively, and root mean square error (RMSE) of reconstructed images obtained by different angles'' projection images was compared. TV-POCS and the reconstruction algorithm based on alternative projection were used to reconstruct mouse vertebra cross section image respectively, and normalized mean square distance (d) and normalized mean absolute distance (r) of two reconstruction algorithms were compared.Results The image reconstructed by CPTV had poorer smoothness and more artifacts. TV-POCS and the reconstruction algorithm based on alternative projection not only suppressed the noise effectively, but also protected the edge of image, which obtained higher image quality. RMSE of the reconstruction algorithm based on alternative projection declined faster than those of other two algorithms, and it had smaller convergence value. The d value and r value of the reconstruction algorithm based on alternative projection were both smaller than TV-POCS (0.064 0 vs 0.262 4, 0.073 7 vs 0.298 2).Conclusion For limited angle projection images, the reconstruction algorithm based on alternative projection can obtain higher image quality and faster convergence speed without parameter estimation.