This paper describes the development of fast Bayesian reconstruction methods for Compton cameras using commodity graphics hardware. For fast iterative reconstruction, not only is it important to increase the convergence rate, but also it is equally important to accelerate the computation of time-consuming and repeated operations, such as projection and backprojection. Since the size of the system matrix for a typical Compton camera is intractably large, it is impractical to use a conventional caching scheme that stores the pre-calculated elements of a system matrix and uses them for the calculation of projection and backprojection. In this paper we propose GPU (graphics processing unit)-accelerated methods that can rapidly perform conical projection and backprojection on the fly. Since the conventional ray-based backprojection method is inefficient for parallel computing on GPUs, we develop voxel-based conical backprojection methods using two different approximation schemes. In the first scheme, we approximate the intersecting chord length of the ray passing through a voxel by the perpendicular distance from the center to the ray. In the second scheme, each voxel is regarded as a dimensionless point rather than a cube so that the backprojection can be performed without the need for calculating intersecting chord lengths or their approximations. Our simulation studies show that the GPU-based method dramatically improves the computational speed with only minor loss of accuracy in reconstruction. With the development of high-resolution detectors, the difference in the reconstruction accuracy between the GPU-based method and the CPU-based method will eventually be negligible.
We propose GPU (graphics processing unit) accelerated methods that can dramatically improve the computational performance of statistical image reconstruction algorithms for Compton cameras. Since the conventional raybased backprojection method is inefficient for GPU, we develop a fully voxel-based backprojection method which can maximize the performance of GPU. In this method, the cone surface is sampled by the evenly distributed rays originated from the vertex of the cone. The intersecting chord length of the ray passing through a voxel is then approximated by the normal distance from the center of the voxel to the ray. Although this approximation can cause an error in backprojection, according to our simulation results, it does not noticeably affect the reconstruction. Our experimental phantom studies with the RAMLA (row-action maximum likelihood algorithm), which is a relaxed version of the OS-EM (ordered subsets expectation maximization) algorithm, indicate that the GPU-based method is roughly 50 times faster in computation time per iteration than the CPU-based method. According to our experimental results, for an acceptable 64×64×64 image reconstructed by RAMLA with 64 subsets and 8 iterations, the CPU-based method takes about 2.3 hours, whereas the GPU-based method takes only 2.7 minutes.
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