Fast PET EM reconstruction from linograms

The approximate discrete Radon transform (ADRT) is a fast forward projection technique for generating linograms. It uses a succession of nearest-neighbor interpolations in a butterfly algorithm analogous to the one used in fast Fourier transforms to gain a (log N)/N speed advantage. We have used matched forward and backward ADRT projectors to perform ML-EM reconstructions for PET (EM-ADRT). Accuracy is tested in three ways. First, linograms of gaussian blobs were generated and reconstructed with 20 iterations of EM-ADRT. Reconstructed blobs in the EM-ADRT images were no more than 0.03 pixels broader than the parent functions, and were mispositioned by no more than a few hundredths of a pixel. The total counts in regions of interest were within 2% of the correct values. Second, Monte-Carlo events for hot and cold spheres in a warm background were separately histogrammed into sinograms and linograms. The sinograms were reconstructed by OSEM, the linograms by EM-ADRT. The two iteratively reconstructed images were of similar quality. All structures in the phantoms were resolved and gray levels were recovered quantitatively. Third, clinical images reconstructed with EM-ADRT have a qualitative appearance similar to OSEM images.