Minimum detection windows, PI-line existence and uniqueness for helical cone-beam scanning of variable pitch.
Minimum detection windows, PI-line existence and uniqueness for helical cone-beam scanning of variable pitch.
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DOI：
10.1118/1.1646041
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发表时间：
2004-03
期刊：
影响因子：
3.8
通讯作者：
Y. Ye;Jiehua Zhu;Ge Wang
中科院分区：
文献类型：
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作者：
Y. Ye;Jiehua Zhu;Ge Wang
本文的目的是研究锥束CT沿着变螺距螺旋线的扫描。首先介绍了变螺距CT重建的基本原理及其在医学成像中的应用。推导了最小检测窗口的计算公式。本文的主要部分证明了这种变螺距螺旋线中PI线存在唯一的一个充分必要条件。这些结果是实现变螺距螺旋线扫描精确重建算法的必要步骤，推广了Katsevich等螺距精确重建公式。通过一个例子表明，当螺距函数的导数不是凸函数时，或者当螺距函数通过一个拐点并开始变慢时，PI线在螺旋圆柱的边缘附近可能不是唯一的。结论是，如果物体被放置在螺旋柱内并且远离其边缘，则对螺距函数的限制较弱，以保持PI线的唯一性。如果物体靠近边缘，则对容许俯仰函数的限制条件变得更强。
The goal of this paper is to study Cone-beam CT scanning along a helix of variable pitch. First the rationale and applications in medical imaging of variable pitch CT reconstruction are explained. Then formulas for the minimum detection window are derived. The main part of the paper proves a necessary and sufficient condition for the existence and uniqueness of PI-lines inside this variable pitch helix. These results are necessary steps toward an exact reconstruction algorithm for helix scanning of variable pitch, generalizing Katsevich's formula on constant pitch exact reconstruction. It is shown through an example that, when the derivative of the pitch function is not convex, or when the pitch function passes a inflection point and begins to slow down, PI-lines may be not unique near the rim of the helix cylinder. The conclusion is that the restriction on the pitch function is weaker, if the object is placed well within the helix cylinder and far from its rim, in order to preserve the uniqueness of PI-lines. If the object is near the rim, the restriction condition on the allowable pitch functions becomes stronger.