发表机构
Lappeenranta–Lahti University of Technology LUT; University of Helsinki; Häme University of Applied Sciences（拉彭兰塔-拉赫蒂理工大学; 赫尔辛基大学; 海梅应用科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将圆环面计算机断层扫描方法应用于实验X射线数据，提出两种框架扩展，引入逐点正性约束，验证其可提升重建质量，支持该方法在实验数据中的适用性。
AI 中文摘要
我们将Ilmavirta、Koskela和Railo在《Torus computed tomography》（SIAM J. Appl. Math., 80(4):1947--1976, 2020）中提出的基于圆环面（torus）的X射线断层扫描方法应用于实验X射线断层扫描数据。该数值实现通过将数据转换为平行束格式，并将投影角度映射到圆环面上的闭合测地线方向，扩展了对扇束测量的适配性。此外，我们考虑了原始框架的两种扩展：Star TCT方法，其可扩展重建的频率覆盖范围；以及Railo在《Fourier analysis of periodic Radon transforms》（J. Fourier Anal. Appl., 26(4):64, 2020）中开发的圆环面反投影的数值实现，我们还为其推导了对应的正则化公式。我们在核桃的实验X射线数据上验证了这些方法，并与滤波反投影进行了比较。我们还引入了逐点正性约束作为后处理步骤，这显著提高了重建精度。我们使用更新后的实现重新进行了模拟数据实验。结果表明，所提出的扩展方法提升了重建质量，支持基于圆环面的重建方法对实验数据的适用性。
英文摘要
Torus computed tomography (Torus CT) reconstructs the Fourier coefficients of an image from X-ray data along closed geodesics on the flat torus. We extend Torus CT to experimental X-ray tomographic data by converting the data to a parallel-beam geometry and mapping the measured projection angles to the geodesic directions on the torus. In addition, we introduce two extensions of the Torus CT framework: the Star TCT method, which recovers additional Fourier coefficients beyond the standard frequency box using the same data, and torus backprojection (TBP), which sums the data over the measured directions. We prove that filtered TBP converges to the Tikhonov-regularized solution for general data up to an explicit error term that vanishes for data which is invariant along fixed geodesics. We also show that the direction-wise averaging of the zero mode is an unbiased estimator and its mean squared error decays like $N^{-2}$. We evaluate the methods on simulated phantoms and experimental X-ray data of a walnut using an updated implementation. The results show that torus-based reconstruction methods are applicable to experimental data, avoid the streak artifacts of filtered backprojection (FBP), and yield competitive reconstruction errors on both simulated and experimental data.
Comments24 pages, 12 figures, 5 tables, new Thm. 2.5, Cor. 2.6-2.7, Prop. 3.1
