1. An arrangement for improving the processing time for systems that include reprojection means, said reprojection means reprojecting initial image data to obtain reprojections for use in correcting for polychromatic artifacts in diagnostic medical images of a subject, said arrangement comprising: (a) scanning means for directing radiation through said subject and detecting an intensity distribution of the radiation traversing the subject; (b) means for providing a set of original projections derived from the detected intensity distribution; (c) back-projector means for back-projecting said set of original projections to provide an original amount of initial image data for an initial image; (d) image processor means for processing a reduced amount of said initial image data into initial image correcting data based on at least two or more constituent tissues having different energy dependent radiation attenuation characteristics; (e) reprojector means for converting a reduced amount of said initial image correcting data into correcting reprojections; (f) means separate from said reprojector means for reducing the original amount of initial image data supplied to said image processor means to speed up the correction operations of said image processor and said reprojector while maintaining the original amount of initial image data; and (g) correction means for connecting said correcting reprojections to said back-projector means to provide image correcting data to correct said initial image data and to thereby provide corrected image data having reduced polychromatic artifact data but having an unreduced amount of image data equal to the amount in said initial image.