Conventional approaches to computed tomography involve scanning the entire cross section and producing an image whose spatial and density resolution is uniform over its entire area. If the extent of each scan is restricted to the width of the lesion being investigated, then the x-ray dose is reduced, but a set of incomplete "truncated" projections is measured. Conversely, projections are "hollow" when their inner parts cannot be measured, e.g., when there is a metallic object within the body cross section. We present procedures for preprocessing incomplete projections so that images can be reconstructed from them using the convolution/back projection method.