Alvarez R E, Stonestrom J P
J Comput Assist Tomogr. 1979 Feb;3(1):77-84. doi: 10.1097/00004728-197902000-00013.
The spatial resolution and noise properties of a computed tomography (CT) image may be altered by two-dimensional linear filtering of the initial image. In this paper, we derive filters that minimize the noise variance subject to a constraint on the spatial resolution. The resulting filter functions can reduce the noise variance by 17% in comparison with conventional filters. The method for obtaining these filters requires knowledge of the noise and imaging properties of the system. We derive theoretical expressions for these properties and introduce experimental techniques for their measurement. The statistical characteristics are shown to be anisotropic, spatially variant, and object dependent. We discuss the implications of this result both for optimal filtering and for the general problem of CT image noise property measurement.
计算机断层扫描（CT）图像的空间分辨率和噪声特性可能会因对初始图像进行二维线性滤波而改变。在本文中，我们推导了在空间分辨率受限的情况下使噪声方差最小化的滤波器。与传统滤波器相比，所得的滤波器函数可将噪声方差降低17%。获取这些滤波器的方法需要了解系统的噪声和成像特性。我们推导了这些特性的理论表达式，并介绍了测量它们的实验技术。统计特性显示为各向异性、空间可变且与物体有关。我们讨论了这一结果对最佳滤波以及CT图像噪声特性测量这一普遍问题的影响。
