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GPU-accelerated 3D Bayesian image reconstruction from Compton scattered data

Van-Giang Nguyen, Soo-Jin Lee, Mi N. Lee
Department of Electronic Engineering, Paichai University, Daejeon, Korea
Physics in Medicine and Biology, 56, Num. 9, 2817

@article{nguyen2011gpu,

   title={GPU-accelerated 3D Bayesian image reconstruction from Compton scattered data},

   author={Nguyen, V.G. and Lee, S.J. and Lee, M.N.},

   journal={Physics in Medicine and Biology},

   volume={56},

   pages={2817},

   year={2011},

   publisher={IOP Publishing}

}

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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. GENERAL SCIENTIFIC SUMMARY. A Compton camera is a 3D emission imaging device consisting of two detectors, a scatterer and an absorber. As the direction of the scattered photon is determined by two detected positions in the scatterer and the absorber, to reconstruct a 3D distribution from Compton scattered data, the incident direction of the emitted photon on the scatterer must be computed within a conical surface of ambiguity. In this paper we propose GPU (graphics processing unit)-accelerated statistical reconstruction methods that can rapidly perform conical projection and backprojection which are the most time-consuming and repeated operations. Since the conventional ray-based backprojection method is inefficient for parallel computing on GPUs, we develop approximated voxel-based conical backprojection methods. Our simulation results demonstrate that the GPU accelerated method dramatically improves the computational speed, thereby making the statistical methods, which provide high-quality reconstructions but suffer from computational problems with conventional CPUs, more practical.
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