Ultra fast 3D incremental backprojection for parallel beam geometries

Abstract

For high resolution PET reconstruction, iterative reconstruction methods, such as OSEM, are widely used. They give relatively good image quality, however reconstruction time is very long. Their reconstruction time prevents daily clinical usage for dynamic (multi-frame) studies. In the iterative EM reconstruction method, Projection and Backprojection are major time consuming parts. Previously the authors presented a new SSP method which improved reconstruction time by orders of magnitude. We developed a new backprojection method by using the incremental concept for 3D Backprojection of parallel beam projection data. In this abstract, we will present the methods for implementing the new incremental concept in 3D Backprojection, and criteria for limitation of Backprojection time. The total number of calculations could be reduced by 3 times in the case of HRRT Backprojector with new incremental algorithm. However, this improvement only reduces processing time by 30%. In the backprojection process, the two main parts can be identified as calculation and saving the calculated result to DRAM. Part of calculation is performed inside of the CPU which is an order of magnitude faster than DRAM access. The most time consuming part was calculation before SSP or the new incremental method were introduced, however, now it has become memory access time to save result. For HRRT reconstruction, ROI parts of the image are 38 MB. This ROI part should be accessed 144 times as number of half view number (when symmetry properties is applied), and 6 times per each view for rotating and adding it back to final image. Total amount of memory access is 38 MB times 144 times 6 = 32 GB. However, most of the current computer system has about 5 GB/sec memory bandwidth which makes memory access time 32/5 = 6.4 sec. This memory access time is almost the same as backprojection time. To overcome this memory bandwidth bottleneck problem, the cluster system should be considered for dynamic studies.