Ultra fast symmetry and SIMD-based projection-backprojection (SSP) algorithm for 3-D PET image reconstruction

Remarkable progress in positron emission tomography (PET) development has occurred in recent years, in hardware, software, and computer implementation of image reconstruction. Recent development in PET scanners such as the high-resolution research tomograph (HRRT) developed by CTI (now Siemens) represents such a case and is capable of greatly enhanced resolution as well as sensitivity. In these PET scanners, the amount of coincidence line data collected contains more than 4.5 x 10(9) coincidence lines of response generated by as many nuclear detectors as 120 000. This formidable amount of data and the reconstruction of this data set pose a real problem in HRRT and have also been of the major bottle neck in further developments of high resolution PET scanners as well as their applications. In these classes of PET scanners, therefore, obtaining one set of reconstructed images often requires many hours of image reconstruction. For example, in HRRT with full data collection in a normal brain scan (using SPAN 3), the image reconstruction time is close to 80 min, making it practically impossible to attempt any list-mode-based dynamic imaging since the image reconstruction time would take many days (as much as 43 h or more for 32-frame dynamic image reconstruction). To remedy this data-handling problem in image reconstruction, we developed a new algorithm based on the symmetry properties of the projection and backprojection processes, especially in the 3-D OSEM algorithm where multiples of projection and back-projection are required. In addition, the single-instruction multiple-data (SIMD) technique also allowed us to successfully incorporate the symmetry properties mentioned above, thereby effectively reducing the total image reconstruction time to a few minutes. We refer to this technique as the symmetry and SIMD-based projection-backprojection (SSP) technique or algorithm and the details of the technique will be discussed and an example of the application of the technique to the HRRT's OSEM algorithm will be presented as a demonstration.