Analytic image reconstruction in PVI using the 3D Radon transform

Algorithms are presented for three-dimensional image reconstruction in positron volume imaging (PVI) using the inversion of the three-dimensional Radon transform (RT). The RT is formed by histogramming events into the planes in which they lie rather than along lines as in the X-ray transform (XT). The authors show the transformation between the RT and the XT, and using this relationship they describe a fast backprojection method for the RT in which the computation time was found to be up to 20 times faster by using the new algorithm. Monte Carlo simulations showed that statistical noise levels in images reconstructed from complete projections with the RT algorithm were comparable to those obtained using the Fourier transform inversion of the XT.<>