Noise Due to Photon Counting Statistics in Computed X-Ray Tomography

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Abstract
A general expression was derived for the noise due to photon counting statistics in computed X-ray tomography. The variance was inversely proportional to the cube of the resolution distance. For scanners using a water box, the noise in the reconstructed image depended inversely on the number of detected primary photons, summed over all angles, that have passed through a resolution element. Predictions of this formula agreed well with the results of computer simulations. How this formula can be used to determine such parameters as required X-ray flux, detector counting rate and dose, with special emphasis on tradeoffs between these parameters and resolution was discussed. It was also shown that to determine the X-ray attenuation coefficient of a resolution element to a given precision, the number of photons required by computed X-ray tomography was close to a theoretical limit.

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