An algorithm is described for three-dimensional (3D) image reconstruction in positron volume imaging (PVI) using the inversion of the 3D radon transform (RT) for a truncated cylindrical detector geometry. A discrete version of the 3D RT is formed in a 3D histogram from the event-line coordinates of the detected events. The histogram entries represent the plane integrals of the activity in the field of view. Conventional inversion of the x-ray transform (XT) excludes oblique events in non-iterative reconstruction methods. by employing a spatially varying angular acceptance of events into the histogrammed plane integrals of the 3D RT, it is possible to include most of the detected oblique events in the reconstruction of the image using the standard 3D RT inversion formula. the oblique events are added to the histogram with a partial weight compared to those in complete (XT) projections. This single-pass reconstruction image has better statistical noise properties than images formed by RT inversion from complete XT projections, but only for some detector geometries is it significantly better. Monte Carlo simulations were used to study the statistical noise in images reconstructed using the new algorithm. The inherent difference in the axial versus the transaxial statistical noise in images reconstructed from truncated detectors is noted and is found to increase by including oblique events with this new algorithm.