SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 1953-1977, December 2023.
Abstract. This paper presents a framework for efficient and accurate computation of X-ray optics, a key ingredient in optimization-based computed tomography (CT) reconstruction algorithms. Based on an algebraic framework for directional convolution in image space and detector space, we construct forward models for X-ray imaging whose computational cost can be optimized for each specific CT geometry. While the framework allows for modeling various sources of blur in the X-ray imaging process for any CT geometry, we demonstrate and characterize its effectiveness in fan-beam and cone-beam geometries with flat detectors. The experiments show improvements in computational efficiency as well as accuracy, in optics calculations and reconstruction error, of the proposed projector compared to the state-of-the-art methods used in forward- and back-projection algorithms.

中文翻译：

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X 射线计算机断层扫描的卷积前向模型

SIAM 影像科学杂志，第 16 卷，第 4 期，第 1953-1977 页，2023 年 12 月。
摘要。本文提出了一个高效、准确计算 X 射线光学的框架，这是基于优化的计算机断层扫描 (CT) 重建算法的关键要素。基于图像空间和探测器空间中定向卷积的代数框架，我们构建了 X 射线成像的正向模型，其计算成本可以针对每个特定的 CT 几何结构进行优化。虽然该框架允许对任何 CT 几何形状的 X 射线成像过程中的各种模糊源进行建模，但我们使用平面探测器证明并表征了其在扇束和锥束几何形状中的有效性。实验表明，与正向和反向投影算法中使用的最先进的方法相比，所提出的投影仪在计算效率以及光学计算和重建误差方面的准确性都有所提高。