Ohkubo Masaki, Wada Shinich, Kobayashi Teiji, Lee Yongbum, Tsai Du-Yih
Department of Radiological Technology, School of Health Sciences, Faculty of Medicine, Niigata University, 2-746 Asahimachi-dori, Niigata-shi, 951-8518, Jap.
Igaku Butsuri. 2004;24(3):115-22.
In the CT image system, we revealed the relationship between line spread function (LSF), or slice sensitivity profile (SSP), and point spread function (PSF). In the system, the following equation has been reported; I(x,y) = O(x,y) ** PSF(x,y), in which I(x,y) and O(x,y) are CT image and object function, respectively, and ** is 2-dimensional convolution. In the same way, the following 3-dimensional expression applies; I'(x,y,z) = O'(x,y,z) *** PSF'(x,y,z), in which z-axis is the direction perpendicular to the x/y-scan plane. We defined that the CT image system was separable, when the above two equations could be transformed into following equations; I(x,y) = [O(x,y) * LSF(x)(x) ] * LSF(y)(y) and I' (x,y,z) = [ O'(x,y,z) * SSP(z) ] ** PSF(x,y), respectively, in which LSF(x)(x) and LSF(y)(y) are LSFs in x- and y-direction, respectively. Previous reports for the LSF and SSP are considered to assume the separable-system. Under the condition of separable-system, we derived following equations; PSF(x,y)=LSF(x)(x) LSF(y)(y) and PSF' (x,y,z) = PSF(x,y) SSP(z). They were validated by the computer-simulations. When the study based on 1-dimensional functions of LSF and SSP are expanded to that based on 2- or 3-dimensional functions of PSF, derived equations must be required.
在CT图像系统中，我们揭示了线扩展函数（LSF）或切片灵敏度分布（SSP）与点扩展函数（PSF）之间的关系。在该系统中，已有如下方程报道：I(x,y) = O(x,y) ** PSF(x,y)，其中I(x,y)和O(x,y)分别为CT图像和物体函数，**表示二维卷积。同样，如下三维表达式也适用：I'(x,y,z) = O'(x,y,z) *** PSF'(x,y,z)，其中z轴是垂直于x/y扫描平面的方向。我们定义，当上述两个方程可分别转化为以下方程时，CT图像系统是可分离的：I(x,y) = [O(x,y) * LSF(x)(x) ] * LSF(y)(y) 和I' (x,y,z) = [ O'(x,y,z) * SSP(z) ] ** PSF(x,y)，其中LSF(x)(x)和LSF(y)(y)分别是x方向和y方向的LSF。先前关于LSF和SSP的报道被认为是假设系统可分离的。在系统可分离的条件下，我们推导出以下方程：PSF(x,y)=LSF(x)(x) LSF(y)(y) 和PSF' (x,y,z) = PSF(x,y) SSP(z)。它们通过计算机模拟得到了验证。当基于LSF和SSP的一维函数的研究扩展到基于PSF的二维或三维函数的研究时，必须要有推导方程。
