An alternative derivation of Katsevich's cone-beam reconstruction formula
An alternative derivation of Katsevich's cone-beam reconstruction formula
复制标题
DOI：
10.1118/1.1628413
复制
发表时间：
2003-12-01
期刊：
影响因子：
3.8
通讯作者：
Chen, GH
中科院分区：
文献类型：
--
作者：
Chen, GH
本文提出了Katsevich锥束图像重建算法的另一种推导方法。出发点是经典的Tuy反演公式。在（i）使用中间函数的隐藏对称性，（ii）通过对冗余数据进行加权来处理冗余数据，（iii）将加权平均值变为对源轨迹参数的积分，以及（iv）对加权函数施加附加约束之后，导出了来自锥束投影的滤波反投影重建公式。本文的主要特点是：第一，放宽了Tuy原始数据充分条件中的非切向条件;其次，提出了一个实用的正则化方案来处理奇异性。第三，锥束情况下的推导与扇束情况下的推导相同。我们最终的锥束重建公式与Katsevich在他最近的论文中发现的公式相同。然而，数据的充分条件和奇异性的正则化方案是不同的。这两种方法之间的详细比较。(C)2003年美国医学物理学家协会。
In this paper an alternative derivation of Katsevich's cone-beam image reconstruction algorithm is presented. The starting point is the classical Tuy's inversion formula. After (i) using the hidden symmetries of the intermediate functions, (ii) handling the redundant data by weighting them, (iii) changing the weighted average into an integral over the source trajectory parameter, and (iv) imposing an additional constraint on the weighting function, a filtered backprojection reconstruction formula from cone beam projections is derived. The following features are emphasized in the present paper: First, the nontangential condition in Tuy's original data sufficiency conditions has been relaxed. Second, a practical regularization scheme to handle the singularity is proposed. Third, the derivation in the cone beam case is in the same fashion as that in the fan-beam case. Our final cone-beam reconstruction formula is the same as the one discovered by Katsevich in his most recent paper. However, the data sufficiency conditions and the regularization scheme of singularities are different. A detailed comparison between these two methods is presented. (C) 2003 American Association of Physicists in Medicine.