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 (logN)/N speed advantage. We have used matched forward and backward ADRT projectors to perform maximum likelihood expectation maximization (ML-EM) reconstructions for PET (EM-ADRT). Speed and accuracy were tested in four ways. First, the speed of EM-ADRT reconstruction was found to be similar to the speed of the ordered subsets expectation maximization (OSEM). Second, sinograms 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. Third, 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. Fourth, clinical images reconstructed with EM-ADRT have a qualitative appearance similar to OSEM images. The EM-ADRT method runs about an order of magnitude faster than ordinary ML-EM on data sets of similar size, and generates accurate reconstructed images. It appears to be accurate in every respect required for clinical 2-D PET, and should be well suited to PET reconstruction based on flat-panel technology.