Noise and contrast detection in computed tomography images.

A discrete representation of the reconstruction process is used in an analysis of noise in computed tomography (CT) images. This model is consistent with the method of data collection in actual machines. An expression is derived which predicts the variance on the measured linear attenuation coefficient of a single pixel in an image. The dependence of the variance on various CT scanner design parameters such as pixel size, slice width, scan time, number of detectors, etc., is then described. The variation of noise with sampling area is theoretically explained. These predictions are in good agreement with a set of experimental measurements made on a range of CT scanners. The equivalent sampling aperture of the CT process is determined and the effect of the reconstruction filter on the variance of the linear attenuation coefficient is also noted, in particular, the choice and its consequences for reconstructed images and noise behaviour. The theory has been extended to include contrast detail behaviour, and these predictions compare favourably with experimental measurements. The theory predicts that image smoothing will have little effect on the contrast-detail detectability behaviour of reconstructed images.