基于广义最小残差算法的非匹配投影矩阵CT迭代图像重建
Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm
摘要：
将广义最小残差（GMRES）算法应用于线性计算机断层成像（CT）模型的图像重建。GMRES算法迭代求解平方非对称线性系统，并且当使用不匹配的反投影仪/投影仪对和应用预处理时，它对CT具有实际应用。GMRES算法被证明在3D CT图像重建问题上，可以看出，使用不匹配的投影矩阵并不妨碍收敛，而在相关的共轭梯度最小二乘（CGLS）算法中使用不匹配的对导致发散迭代。使用GMRES预处理的实施也被证明。
英文摘要：
The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application to CT when using unmatched back-projector/projector pairs and when applying preconditioning. The GMRES algorithm is demonstrated on a 3D CT image reconstruction problem where it is seen that use of unmatched projection matrices does not prevent convergence, while using an unmatched pair in the related conjugate gradients for least-squares (CGLS) algorithm leads to divergent iteration. Implementation of preconditioning using GMRES is also demonstrated.
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