3D PET image reconstruction with on-the-fly system matrix generation accelerated by utilizing shift and symmetry properties.

The use of small crystals in new PET scanners results in large number of line-of-response (LOR). Thus, fully 3D image reconstruction becomes time consuming, especially for iterative algorithms such as Ordered Subset EM (OSEM). In this paper, we describe a method to speed-up the calculation of OSEM by utilizing shift and symmetric properties of crystal arrangement in the scanner. We name this method as Shift Symmetry OSEM (SS-OSEM). With SS-OSEM, calculation of system matrix for different LORs can be done by simply reversing, exchanging, and shifting the index in the object space. This significantly reduces the number of LOR needed to be ray-traced. We implement SS-OSEM for the jPET-D4 which is a novel four-layered DOI scanner. We found out that SS-OSEM is about 10 times faster than non shift-symmetric version. Then, we expand the implementation with parallel computing by using the MPI library. With 16 parallel threads on four node cluster, we are able to achieve 12 times speed-up in the computation. Several implementation issues and restriction for SS-OSEM are also discussed. With parallel implementation of SS-OSEM, we show that it is possible to obtain a fully 3D reconstructed image within clinically acceptable time for scanner with large number of LOR such as the jPET-D4.Fully Three-Dimensional Image Reconstruction Meeting in Radiology and Nuclear Medicin