ABSTRACT This study newly demonstrates a compressed sensing (CS)-based reconstruction scheme for computed tomography (CT) with a translational trajectory. CT with a translational trajectory has many potential applications in the field of non-destructive testing (NDT) and medicine. For example, in the X-ray inspection of a large civil engineering structure, the movements of the source and detector are strictly limited, and a simple straight CT trajectory is preferable. This method could also be applied in X-ray inspection lines in factories and airports. In the medical field, this method would complement the tomosynthesis in mammography. When using a translational trajectory, the dispersion of the fan- or cone-beam creates projection data with the angular information of the sample object. However, the angular information inevitably becomes insufficient when using a translational trajectory, which degrades the reconstruction accuracy. In this case, CS is considered suitable for reconstruction because it has been successfully used for reconstructions from sparse-view and limited-angle data. For reconstruction from the translational trajectory projection, a new concept of directional difference (DD) regularization was proposed. An algorithm was developed based on the alternating direction method of multipliers (ADMM) algorithm to solve the regularization problem. Numerical reconstruction experiments from noisy projection data were conducted and the results were compared with those from other reconstruction methods. The convergence performance of the total variation (TV), DD, and mixed TV-DD regularization methods were examined. The proposed DD and TV-DD methods showed better performance than the TV only regularization. Reconstruction from Monte-Carlo simulated projection data was also demonstrated.

中文翻译：

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基于压缩感知的具有平移轨迹的计算机断层扫描重建

摘要 这项研究新近展示了一种基于压缩感知 (CS) 的具有平移轨迹的计算机断层扫描 (CT) 重建方案。具有平移轨迹的 CT 在无损检测 (NDT) 和医学领域具有许多潜在的应用。例如，在大型土木工程结构的X射线检查中，源和探测器的运动受到严格限制，最好是简单的直线CT轨迹。这种方法也可以应用于工厂和机场的X射线检测线。在医学领域，这种方法将补充乳房 X 线照相术中的断层合成。使用平移轨迹时，扇形或锥形光束的色散会使用样本对象的角度信息创建投影数据。然而，当使用平移轨迹时，角度信息不可避免地变得不足，这会降低重建精度。在这种情况下，CS 被认为适合重建，因为它已成功用于从稀疏视图和有限角度数据的重建。为了从平移轨迹投影重建，提出了方向差异（DD）正则化的新概念。提出了一种基于乘法器交替方向法（ADMM）算法来解决正则化问题的算法。进行了噪声投影数据的数值重建实验，并将结果与​​其他重建方法的结果进行了比较。检查了总变异 (TV)、DD 和混合 TV-DD 正则化方法的收敛性能。所提出的 DD 和 TV-DD 方法表现出比仅 TV 正则化更好的性能。还演示了从蒙特卡罗模拟投影数据重建。