Phys. Med. Biol., zyxwvutsr 1987, Vol. zyxwvutsr 32, No 5, 565-575. Printed in the UK The noise power spectrum of CT images Marie Foley Kijewski and Philip F Judy Department of Radiology, Harvard Medical School and Brigham and Women’s Hospital, Boston, Massachusetts 02115, USA Received 22 July 1986 Abstract. Anexpression for the noise power spectrum of images reconstructed by the discrete filtered backprojection algorithm has been derived. Theformulationexplicitly includes sampling within the projections, angular sampling, and the two-dimensional sampling implicit in the discrete representation of the image. The effects of interpolation are also considered. Noise power spectra predicted by this analysis differ from those predicted using continuous theory in two respects: they are rotationally asymmetric, and they do not approach zero at zero frequency. Both of these properties can be attributed totwo-dimensionalaliasingduetopixelsampling. The predictionswereconfirmedby measurement of noise power spectra of both simulated images and images from a commer- cial x-ray transmission CT scanner. 1. Introduction The quality of computed tomographic (CT) images is usually evaluated in terms of spatial resolution and level of noise. A single-parameter measure of image noise, however,suchas the standard deviationover an area, is inadequate to predict the utility of an image for a given task. Riederer zyxw et zyxwvu al (1978) showed that the random variation in CT number at one point of an image is not independent of the random variation at other points. These spatial correlations can be fully described by either the autocorrelation function or its Fourier transform, the noise power spectrum zy ( NPS) (Dainty and Shaw 1974). Riederer er al (1978) used the continuous convolution-backprojection model to predict the image NPS from the projection NPS, under the assumption that the noise in theprojections is uncorrelated (white). The image NPS was analysed in light of decision theory by Wagner et zyxwvuts a1 (1979) and by Hanson (1979), also using continuous variables. These authors concluded that the shape of the NPS is determined by the reconstruction algorithm, specifically the convolution filter, and that, consequently, the image NPS is rotationally symmetric and proportional to frequency at low frequencies. For discrete backprojection, the reconstruction algorithm includes sampling and interpolation,as well as filtering and backprojection. Faulkner and Moores (1984) derived a formula which represented the NPS for a discrete reconstruction process. Although they considered sampling within the projections and angular sampling, they neglected both the interpolation and the two-dimensional sampling intrinsic to discrete backprojection. The formula which they derived for the NPS resulting from discrete convolution-backprojection was equivalent to those derived previously for continuous 0031-9155/87/050565+ 11$02.50 @ 1987 IOP Publishing Ltd 565