AI 中文总结
针对X射线CT中投影器不匹配致重建问题数学性质改变及影响迭代方法收敛的情况，开发AB和BA - GKB算法的混合变体，利用奇异值分解重建解并自动选正则化参数，经实验验证该混合方法能提高抗半收敛鲁棒性。
AI 中文摘要
X射线计算机断层扫描（CT）在医学、工业和科学应用中是一种广泛使用的成像方式。在实际CT实现中，正向算子A和反向投影算子B通常使用不同的离散化方案构建，导致反投影器通常与正向投影器不匹配，这改变了重建问题的数学性质并影响迭代重建方法的收敛行为。以往研究提出了AB和BA Golub Kahan双对角化（GKB）方法等。本文通过在投影过程中纳入正则化来开发AB - 和BA - GKB算法的混合变体，利用投影空间上算子的奇异值分解有效重建解，并使用L曲线或广义交叉验证自动选择正则化参数。数值实验证明了所提混合方法在提高抗半收敛鲁棒性方面的有效性。
英文摘要
X ray Computed Tomography (CT) is a widely used imaging modality in medical, industrial, and scientific applications. In practical CT implementations, forward, A, and back projection, B, operators are often constructed using different discretization schemes to improve computational efficiency on available software and hardware platforms. Consequently, the resulting projector pair is generally unmatched, meaning that the back projector is not the exact adjoint of the forward projector. This mismatch alters the mathematical properties of the reconstruction problem and can affect the convergence behavior of iterative reconstruction methods. Previous studies have proposed AB and BA Golub Kahan bidiagonalization (GKB) methods, as well as GMRES and hybrid GMRES methods, for solving CT reconstruction problems with unmatched projector pairs, demonstrating reduced semiconvergence effects compared with conventional approaches. In this work, we develop hybrid variants of the AB- and BA-GKB algorithms by incorporating regularization within the projection process. The singular value decomposition for the operator on the projected space is used to efficiently reconstruct the solution, and to automatically select the regularization parameter using either the L-curve or generalized cross-validation. Numerical experiments on several CT reconstruction problems demonstrate the effectiveness of the proposed hybrid methods in improving robustness against semiconvergence.
