Analysis of x-ray computed tomography images using the noise power spectrum and autocorrelation function

A discrete representation of the reconstruction process, consistent with the method of data collection, has been used to derive expressions for the noise power spectrum, autocorrelation function and noise equivalent quanta (NEQ) of a computed tomography (CT) image. These parameters have been expressed in terms of basic scanning factors such as tube current, exposure time, slice width and number of detectors. Each of these factors affects the overall magnitude of the noise power spectrum, but the spatial frequency dependence is also determined by the type of reconstruction filter used in the computer algorithm. The noise power spectrum has been calculated for scanners employing either a ramp or Hanning weighted ramp filter. Predictions made from this theoretical analysis have been compared with experimental measurements made on various CT scanners. Measurements were made of the modulation transfer function (MTF) by techniques which permitted us to deduce the contributions of the algorithmic and non-algorithmic components to the overall MTF. NEQ values have been calculated for a number of CT scanners.