The question of what spatial frequency response gives optimum image quality in computed tomography (CT) images is studied. We have developed a technique for smoothing these images by using a modified back projection filter with attenuated high frequency response. The results are images with a blurred appearance but dramatically reduced image noise. On processing raw data from the EMI head scanner in this way, grey and white matter distributions are clearly visualized with no increase in radiation dose. These results are analyzed in terms of the Weiner spectrum and correlation properties of CT noise. In particular, a "noise equivalent aperture" is defined in a way analogous to that of Schade. It is shown that the prediction of the simple Rose model of noise sampling cannot explain the improvement produced by smoothing, even when the correlated character of the noise is taken into account.