Relationship between line spread function (LSF), or slice sensitivity profile (SSP), and point spread function (PSF) in CT image system

Abstract

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.