Exact gram filtering and efficient backprojection for iterative CT reconstruction
Exact gram filtering and efficient backprojection for iterative CT reconstruction
复制标题
用于迭代 CT 重建的精确克过滤和高效反投影
DOI：
10.1002/mp.15547
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发表时间：
2022
期刊：
影响因子：
3.8
通讯作者：
Entezari, Alireza
中科院分区：
文献类型：
--
作者：
Shu, Ziyu;Entezari, Alireza
前向和后向投影是所有基于模型的迭代重建（MBIR）方法的基础。然而，精确地计算这些是耗时的。在本文中，我们提出了一种方法MBIR在平行X射线束几何，利用一个革兰氏滤波器，有效地实现正向和反向projection.MethodsWe建议使用体素的基础上，并在一个盒样条框架中建模其足迹准确计算的革兰氏滤波器，提高反投影的性能。在平行X射线束几何形状的特殊情况下，如果正弦图信号是带限的，则可以通过估计的Gram滤波器有效地实现前向和反向投影。本文提出了一种专门的正弦图插值方法，消除了带宽限制的前提条件，从而提高了重建精度。我们在此基础上，利用体素基足迹的连续性，提供更精确的正弦图插值，进一步提高反投影的效率和质量。此外，检测器模糊的效果可以有效地占在我们的方法，以更好地处理现实scenaries.ResultsThe所提出的方法进行测试，在不同的分辨率，正弦图采样步骤，和噪声水平下的幻影和真实的计算机断层扫描（CT）图像。所提出的方法始终优于其他国家的最先进的投影模型的速度和精度方面的反投影和reconstruction.ConclusionsWe提出了一种迭代重建方法的三维平行束X射线CT重建。我们的实验结果表明，所提出的方法准确、快速且可重复，并且在反投影和重建结果方面显着优于其他最先进的投影模型。
PurposeForward and backprojections are the basis of all model‐based iterative reconstruction (MBIR) methods. However, computing these accurately is time‐consuming. In this paper, we present a method for MBIR in parallel X‐ray beam geometry that utilizes a Gram filter to efficiently implement forward and backprojection.MethodsWe propose using voxel‐basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of backprojection. In the special case of parallel X‐ray beam geometry, the forward and backprojection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel‐basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of backprojection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realistic scenarios.ResultsThe proposed method is tested on both phantom and real computed tomography (CT) images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state‐of‐the‐art projection models in terms of speed and accuracy for both backprojection and reconstruction.ConclusionsWe proposed a iterative reconstruction methodology for 3D parallel‐beam X‐ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state‐of‐the‐art projection models on both backprojection and reconstruction results significantly.