National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, Japan.
J Xray Sci Technol. 2018;26(5):691-705. doi: 10.3233/XST-18378.
Cylindrical phantoms are often imaged by X-ray computed tomography (CT) to evaluate the extent of beam hardening (or cupping artifact) resulting from a polychromatic X-ray source.
Our goal was to derive analytical expressions for the reconstructed image of a homogeneous cylindrical phantom exhibiting a cupping artifact, to permit a quantitative comparison with experimental cupping data.
A filtered backprojection method was employed to obtain the analytical cupping profile for the phantom, assuming that the projection data could be approximated as a power series with respect to the sample penetration thickness.
The cupping profile was obtained analytically as a series of functions by employing Ramachandran filtering with an infinite Nyquist wavenumber. The quantitative relationship between the power series of the projection and the nth moment of the linear attenuation coefficient spectrum of the phantom was also determined. Application of the obtained cupping profile to the evaluation of the practical reconstruction filters with a finite Nyquist wavenumber and to the best choice of the contrast agent was demonstrated.
The set of exact solutions derived in this work should be applicable to the analysis of cylindrical phantom experiments intended to evaluate CT systems.
圆柱型体模常用于 X 射线计算机断层扫描（CT）成像，以评估多色 X 射线源导致的束硬化（或杯状伪影）程度。
我们的目标是推导出具有杯状伪影的均匀圆柱型体模的重建图像的解析表达式，以便与实验杯状数据进行定量比较。
采用滤波反投影法获得体模的解析杯状轮廓，假设投影数据可以近似为关于样本穿透厚度的幂级数。
通过采用具有无限奈奎斯特波数的拉马钱德兰滤波，将杯状轮廓解析为一系列函数。还确定了投影的幂级数与体模线性衰减系数谱的第 n 阶矩之间的定量关系。应用获得的杯状轮廓评估具有有限奈奎斯特波数的实际重建滤波器和对比剂的最佳选择进行了演示。
本文推导的这组精确解应该适用于分析旨在评估 CT 系统的圆柱型体模实验。
