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Iterative image reconstruction algorithms based on a stochastic model of emission tomography have been widely studied, because they can provide better image quality than analytic reconstruction algorithms. However, their long reconstruction time has been a major bottle neck for further developments of high resolution PET scanners and their applications. In recent years, there have been several attempts to reduce the PET image reconstruction time by using a graphic processing unit (GPU). To obtain high computational performance on a massive parallel GPU, however, global memory coalescing and branching diversity are to be carefully considered, which are not considered in most existing GPU-based algorithms. To increase global memory coalescing, we propose the image-rotation-based (IR-based) projection and frame-rotation-based (FR-based) backprojection schemes. We then successfully incorporate the geometrical symmetry property into the proposed schemes to reduce the branching diversity. Thereby, we effectively reduce the total image reconstruction time from many hours to a few seconds. Experimental results show that the proposed algorithm reduces the computation time by a factor of about 539 compared with a CPU-based straightforward implementation.