Use of a fast EM algorithm for 3D image reconstruction with the YAP–PET tomograph

Objective. We would like to improve the image reconstructions for both signal-to-noise ratio (SNR) and spatial resolution characteristics for the small animal positron emission tomograph YAP–PET, built at the Department of Physics of Ferrara University. The three-dimensional (3D) filtered backprojection (FBP) algorithm, usually used for image reconstruction, has a limited angle restriction due to the tomograph geometry, which causes a serious loss in sensitivity. Methods. We implemented a 3D iterative reconstruction program using the symmetry and sparse properties of the ‘probability matrix’, which correlates the emission from each voxel to the detector within a coincidence tube. A fraction only of matrix elements are calculated before the reconstruction and stored on disk: this allows us to avoid on-line computation. A depth dependent function differentiates the voxels in a coincidence tube. Three experimental phantoms with no background were reconstructed by using the program, in comparison with traditionally used FBP. Results. The adopted method allowed us to reduce the computation time significantly. Furthermore, the simple depth dependent function improved the spatial resolution. With 64×64×20 voxels of 0.625×0.625×2.0 mm 3 in the field of view, the computation time was less than 4 min per iteration on a Sparc Ultra450 Workstation, and less than 6 min per iteration on a Mac-PPC G3 300 MHz: the spatial resolution measured with a 0.8 mm diameter 18F-FDG filled capillary reconstructed in this way was 2.0 mm FWHM. By decreasing the voxel size to 0.3125×0.3125×2.0 mm 3 per voxel the transaxial FWHM was 1.7 mm with a computation time of 15 min per iteration on a Sparc Ultra450. By using all the acquired data, the SNR improves from 1.3 to 6.0 in the worst measured case, a pair of 0.8 mm diameter 18F-FDG filled capillaries, which are 2.5 mm apart each other. Conclusion. The adoption of iterative reconstruction allowed us to overcome the loss in sensitivity of previously used FBP: this improved the SNR. The studies of symmetry and sparse properties avoided a severe increase of the reconstruction time and of storing space on disk. This fast EM Algorithm is now routinely used for the image reconstruction with the YAP–PET tomograph.