The resolution of an image produced by a CT imaging system is increased by employing an image reconstruction method that takes advantage of the redundant attenuation measurements made during a typical scan. An initial image is reconstructed with a filtered backprojection technique using the projection views acquired during the scan. Further images of higher resolution are produced by an iterative process in which the reconstructed image is reprojected, combined with originally acquired projection data, and backprojected again at the higher resolution.