A general exact method for synthesizing parallel-beam projections from cone-beam projections via filtered backprojection
A general exact method for synthesizing parallel-beam projections from cone-beam projections via filtered backprojection
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DOI：
10.1088/0031-9155/51/21/017
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发表时间：
2006-10
影响因子：
3.5
通讯作者：
Liang Li;Zhiqiang Chen;Yuxiang Xing;Li Zhang;Kejun Kang;Ge Wang
中科院分区：
文献类型：
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作者：
Liang Li;Zhiqiang Chen;Yuxiang Xing;Li Zhang;Kejun Kang;Ge Wang
近年来，锥形束计算机断层扫描（CT）的图像重建方法得到了广泛的研究。然而，这些研究很少讨论从锥形束投影计算平行束投影。在本文中，我们重点关注锥束投影的完整或不完整平行束投影的精确合成。首先，描述扩展中心切片定理以建立氡空间和傅里叶空间之间的关系。然后，提出了从锥形束数据计算平行束投影数据的数据充分性条件。利用这些结果，制定了通用的滤波反投影算法，该算法可以从锥形束投影数据精确地合成平行束投影数据。作为一个例子，我们证明了在圆锥光束扫描的情况下，可以在一定角度范围内精确地合成平行光束投影。有趣的是，这个角度范围大于 Feldkamp 重建框架中得出的角度范围。在圆形扫描情况下进行数值实验来验证我们的方法。
In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been extensively studied. However, few of these studies discussed computing parallel-beam projections from cone-beam projections. In this paper, we focus on the exact synthesis of complete or incomplete parallel-beam projections from cone-beam projections. First, an extended central slice theorem is described to establish a relationship between the Radon space and the Fourier space. Then, data sufficiency conditions are proposed for computing parallel-beam projection data from cone-beam data. Using these results, a general filtered backprojection algorithm is formulated that can exactly synthesize parallel-beam projection data from cone-beam projection data. As an example, we prove that parallel-beam projections can be exactly synthesized in an angular range in the case of circular cone-beam scanning. Interestingly, this angular range is larger than that derived in the Feldkamp reconstruction framework. Numerical experiments are performed in the circular scanning case to verify our method.