Chesler D A, Riederer S J, Pelc N J
J Comput Assist Tomogr. 1977 Jan;1(1):64-74. doi: 10.1097/00004728-197701000-00009.
A general expression is derived for the noise due to photon counting statistics in computed X-ray tomography. The variance is inversely proportional to the cube of the resolution distance. For scanners using a water box, the noise in the reconstructed image depends inversely on the number of detected primary photons, summed over all angles, that have passed through a resolution element. Predictions of this formula agree well with the results of computer simulations. It is shown how this formula can be used to determine such parameters as required X-ray flux, detector counting rate, and dose, with special emphasis on tradeoffs between these parameters and resolution. It is also shown that to determine the X-ray attenuation coefficient of a resolution element to a given precision, the number of photons required by computed X-ray tomography is close to a theoretical limit.
推导了计算机X射线断层扫描中由于光子计数统计产生的噪声的一般表达式。方差与分辨率距离的立方成反比。对于使用水箱的扫描仪，重建图像中的噪声反比于通过分辨率单元的所有角度上检测到的初级光子数量之和。该公式的预测结果与计算机模拟结果吻合良好。展示了如何使用该公式确定所需的X射线通量、探测器计数率和剂量等参数，特别强调了这些参数与分辨率之间的权衡。还表明，为了将分辨率单元的X射线衰减系数确定到给定精度，计算机X射线断层扫描所需的光子数量接近理论极限。
