arXiv 2402.044802024-02eess.IVcs.CVmath.OC

SAMCIRT：一种用于四维计算机断层扫描（4DCT）的同时重建与仿射运动补偿技术

SAMCIRT: A Simultaneous Reconstruction and Affine Motion Compensation Technique for Four Dimensional Computed Tomography (4DCT)

University of Antwerp（安特卫普大学）；Phenikaa University（费因基亚大学）；Institut de Mathématiques de Jussieu – Paris Rive Gauche（巴黎右岸数学研究所）；Silverhead Innovation Strategies and Solutions SAS（Silverhead创新策略与解决方案SAS）

Anh-Tuan Nguyen, Jens Renders, Khoi-Nguyen Nguyen, Tat-Dat To, Domenico Iuso, Yves Maris

备注：: 25 pages, revised version submitted to the SIAM Journal on Imaging Sciences (SIIMS)

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AI总结：

针对4DCT中迭代方法计算复杂且缺乏收敛证明及工具缺乏仿射运动解析伴随的问题，提出SAMCIRT，在单步更新中结合重建与仿射运动估计，证明分离Lipschitz连续性保证收敛，实验优于现有方法并实现真实钻石重建。

摘要：

近期大多数四维计算机断层扫描（4DCT）迭代方法不仅依赖于嵌套迭代，从而增加了计算复杂度并限制了潜在的加速，而且未能为其提出的迭代方案提供收敛性的理论证明。另一方面，最新的MATLAB和Python图像处理工具箱缺乏对三维物体体积的仿射运动算子解析伴随的实现，这不允许使用针对仿射运动参数的精确导数的梯度方法。在这项工作中，我们提出了同时仿射运动补偿图像重建技术（SAMCIRT）——一种高效的迭代重建方案，该方案基于运动算子的解析伴随，然后在单个更新步骤中结合图像重建和仿射运动估计，并分别对重建参数和仿射运动参数求精确偏导数。此外，我们证明了目标函数及其相关函数（包括梯度）的分离Lipschitz连续性，这支持了我们提出的迭代方案的收敛性，尽管目标函数关于仿射运动参数是非凸的。仿真和真实实验的结果表明，我们的方法在计算可行性和投影距离方面优于最先进的带仿射运动校正的CT重建方法。特别是，这允许对真实的、非平稳的钻石进行精确重建，展示了4DCT的一种新颖应用。

英文摘要：

The majority of the recent iterative approaches in 4DCT not only rely on nested iterations, thereby increasing computational complexity and constraining potential acceleration, but also fail to provide a theoretical proof of convergence for their proposed iterative schemes. On the other hand, the latest MATLAB and Python image processing toolboxes lack the implementation of analytic adjoints of affine motion operators for 3D object volumes, which does not allow gradient methods using exact derivatives towards affine motion parameters. In this work, we propose the Simultaneous Affine Motion-Compensated Image Reconstruction Technique (SAMCIRT)- an efficient iterative reconstruction scheme that combines image reconstruction and affine motion estimation in a single update step, based on the analytic adjoints of the motion operators then exact partial derivatives with respect to both the reconstruction and the affine motion parameters. Moreover, we prove the separated Lipschitz continuity of the objective function and its associated functions, including the gradient, which supports the convergence of our proposed iterative scheme, despite the non-convexity of the objective function with respect to the affine motion parameters. Results from simulation and real experiments show that our method outperforms the state-of-the-art CT reconstruction with affine motion correction methods in computational feasibility and projection distance. In particular, this allows accurate reconstruction for a real, nonstationary diamond, showing a novel application of 4DCT.

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