Analytic image reconstruction in PVI using the 3D Radon transform

Algorithms have been derived for 3-D image reconstruction in positron volume imaging (PVI) using the inversion of the 3-D Radon transform (RT) for a truncated cylindrical detector geometry. The RT is formed by histogramming events according to the planes in which they lie, with a weight determined by an angular acceptance function. A fast backprojection method for the RT is described in which the computation time is found to be up to 20 times faster with the new algorithm compared to the traditional X-ray transform (XT) backprojection method. Monte Carlo simulations show that statistical noise levels in images reconstructed from complete projections with the new RT algorithm are comparable to those obtained using the Fourier transform inversion of the XT.<>