A simple theorem relating noise and patient dose in computed tomography

Presented is a simple model describing the dependence of image noise in computed tomography on the x-ray beam profile. The model is used to derive the x-ray profile which minimizes total image noise at constant integral patient dose. The profile may be produced with a bow-tie-type beam shaping filter. Results of the analysis are validated using a computer simulation of computed tomography (CT) acquisition and reconstruction.