1. In a fan beam computed tomographic system having a detector system for taking a plurality of projections at a plurality of angles, each projection defining a plurality of projection bins, the computed tomographic system having a given center of rotation which is shifted from the midline of the fan by a predetermined shift distance, a method of compensating for the shift in performing the computed tomographic reconstruction comprising the steps of, producing a non-constant series of weighting functions, one for each projection bin in the fan beam projection sets and which are dependent on the detector geometry and the magnitude of the shift; weighting the information in each projection bin in the fan beam projection sets with its associated weighting function to produce corrected fan beam projection sets, convolving the corrected fan beam projection sets with a filter function to produce convolved corrected fan beam projection sets, setting up a coordinate system in pixelized space located with respect to said pixelized space to take account of the shift, and back projecting the convolved corrected fan beam projection sets into the pixelized space using said coordinate system to produce a CT image corrected for the shift.