Filtered backprojection formula for exact image reconstruction from cone-beam data along a general scanning curve
Filtered backprojection formula for exact image reconstruction from cone-beam data along a general scanning curve
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DOI：
10.1118/1.1828673
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发表时间：
2005-01-01
期刊：
影响因子：
3.8
通讯作者：
Wang, G
中科院分区：
文献类型：
--
作者：
Ye, YB;Wang, G
最近，Katsevich证明了一个滤波反投影公式，用于从锥束数据沿沿着轨迹精确重建图像，这是自1991年螺旋锥束扫描模式提出以来的一个重要突破。在本文中，我们证明了广义Katsevich的公式，从锥束数据收集沿着一个相当灵活的曲线精确的图像重建。我们还将给出滤波方向的一般条件。基于这个条件，我们提出了一个自然选择的滤波方向，这是更方便，比Katsevich的选择，可以适用于一般的扫描曲线。在推导过程中，我们使用分析技术，而不是几何参数。因此，我们不需要PI线的唯一性。事实上，我们的公式可以用于重建任何弦上的图像，只要扫描曲线从弦的一端延伸到另一端。这可以看作是奥尔洛夫经典定理的推广。具体来说，我们的公式可以应用于（i）可变半径和螺距的非标准螺旋（PI或n-PI窗口），和（ii）鞍形曲线。(C)2005年美国医学物理学家协会。
Recently, Katsevich proved a filtered backprojection formula for exact image reconstruction from cone-beam data along a helical scanning locus, which is an important breakthrough since 1991 when the spiral cone-beam scanning mode was proposed. In this paper, we prove a generalized Katsevich's formula for exact image reconstruction from cone-beam data collected along a rather flexible curve. We will also give a general condition on filtering directions. Based on this condition, we suggest a natural choice of filtering directions, which is more convenient than Katsevich's choice and can be applied to general scanning curves. In the derivation, we use analytical techniques instead of geometric arguments. As a result, we do not need the uniqueness of the PI lines. In fact, our formula can be used to reconstruct images on any chord as long as a scanning curve runs from one endpoint of the chord to the other endpoint. This can be considered as a generalization of Orlov's classical theorem. Specifically, our formula can be applied to (i) nonstandard spirals of variable radii and pitches (with PI- or n-PI-windows), and (ii) saddlelike curves. (C) 2005 American Association of Physicists in Medicine.