Duerinckx A J, Macovski A
J Comput Assist Tomogr. 1979 Aug;3(4):519-26. doi: 10.1097/00004728-197908000-00015.
The variance of the image noise in computed X-ray transmission tomography (CT) due to quantum noise is in a first approximation a nonlinear function of X-ray attenuation. Beam hardening in CT is also a nonlinear function of attenuation. We present a theoretical study of both phenomena. Computer simulations and numerical results show that both nonlinear dependencies have quite similar effects on image quality. We also show how the two-dimensional distribution of the noise variance in a CT image is a weighted superposition of images obtained by backprojecting integer powers of the noiseless projection data corresponding to the scanned object. The streak-like pattern in the image noise due to the anisotropic nature of the noise cross-correlation function is discussed. We also discuss how these nonlinear phenomena affect noise filtering and tissue characterization using statistical parameters.
在计算机X射线透射断层扫描（CT）中，由于量子噪声导致的图像噪声方差在一阶近似下是X射线衰减的非线性函数。CT中的束硬化也是衰减的非线性函数。我们对这两种现象进行了理论研究。计算机模拟和数值结果表明，这两种非线性相关性对图像质量的影响非常相似。我们还展示了CT图像中噪声方差的二维分布是如何通过对与扫描对象对应的无噪声投影数据的整数幂进行反投影得到的图像的加权叠加。讨论了由于噪声互相关函数的各向异性导致的图像噪声中的条纹状图案。我们还讨论了这些非线性现象如何使用统计参数影响噪声滤波和组织表征。
