Schaller S, Sauer F, Tam K C, Lauritsch G, Flohr T
Siemens Medizinische Technik, Forchheim, Germany.
IEEE Trans Med Imaging. 2000 May;19(5):361-75. doi: 10.1109/42.870247.
This paper addresses the long object problem in helical cone-beam computed tomography. We present the PHI-method, a new algorithm for the exact reconstruction of a region-of-interest (ROI) of a long object from axially truncated data extending only slightly beyond the ROI. The PHI-method is an extension of the Radon-method, published by Kudo, Noo, and Defrise in issue 43 of journal Physics in Medicine and Biology. The key novelty of the PHI-method is the introduction of a virtual object fpsi(x) for each value of the azimuthal angle psi in the image space, with each virtual object having the property of being equal to the true object f(x) in some ROI omegam. We show that, for each psi, one can calculate exact Radon data corresponding to the two-dimensional (2-D) parallel-beam projection of fpsi(x) onto the meridian plane of angle psi. Given an angular range of length pi of such parallel-beam projections, the ROI omegam can be exactly reconstructed because f(x) is identical to fpsi(x) in Omegam. Simulation results are given for both the Radon-method and the PHI-method indicating that 1) for the case of short objects, the Radon- and PHI-methods produce comparable image quality, 2) for the case of long objects, the PHI-method delivers the same image quality as in the short object case, while the Radon-method fails, and 3) the image quality produced by the PHI-method is similar for a large range of pitch values.
本文探讨螺旋锥束计算机断层扫描中的长物体问题。我们提出了PHI方法，这是一种新算法，用于从仅略微超出感兴趣区域（ROI）轴向截断的数据中精确重建长物体的ROI。PHI方法是Kudo、Noo和Defrise在《医学与生物学物理》杂志第43期发表的Radon方法的扩展。PHI方法的关键创新之处在于，在图像空间中为方位角psi的每个值引入了一个虚拟物体fpsi(x)，每个虚拟物体在某个ROI omegam中具有与真实物体f(x)相等的属性。我们表明，对于每个psi，可以计算出与fpsi(x)在角度psi的子午面上的二维（2-D）平行束投影相对应的精确Radon数据。给定这样的平行束投影的长度为pi的角度范围，ROI omegam可以被精确重建，因为f(x)在Omegam中与fpsi(x)相同。给出了Radon方法和PHI方法的模拟结果，表明：1）对于短物体的情况，Radon方法和PHI方法产生的图像质量相当；2）对于长物体的情况，PHI方法提供与短物体情况相同的图像质量，而Radon方法失败；3）PHI方法在大范围的螺距值下产生的图像质量相似。
