GPU通用计算在CT中的应用
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摘要
伴随着PC级微机的崛起和普及，多年来计算机图形处理器(graphics processing unit，简称GPU)以大大超过摩尔定律的速度高速发展。图形处理器的发展极大地提高了计算机图形处理的速度和图形质量，并促进了与计算机图形相关应用领域的快速发展。与此同时，图形处理器绘制流水线的高速度和并行性以及近年来发展起来的可编程功能为图形处理以外的通用计算提供了良好的运行平台，这使得基于GPU的通用计算成为近两三年来人们关注的一个研究热点。
在CT领域，GPU通用计算技术同样有很大的应用空间，越来越多的人开始研究GPU通用计算技术在CT中的应用，本文利用GPU通用计算技术实现了三维CT数据的仿真。用CPU进行三维数据的仿真，其仿真速度比较慢，而且模型越复杂所花费的时间越多。由于图像的渲染过程与CT的数据扫描过程很相似，受此启发，本文把CT数据扫描的过程看作图像渲染的过程，利用GPU通用计算技术在GPU上实现了CT数据仿真。实验数据表明用GPU进行数据仿真与传统的CPU进行CT数据的仿真效率得到大大提升。同样道理把CT重建的过程可以看作投影的反过程，受此启发，本文利用GPU通用计算技术实现了平行扇束CT图像重建，其中投影数据是256~*256，360个角度投影，重建体大小是256~*256~*256，测试结果表明GPU上重建时间比CPU下重建时间快了4倍左右。
本文还利用GPU通用计算技术实现了快速傅立叶变换并将结果应用到CT滤波反投影重建算法中，将滤波反投影算法统一在GPU进行。实验数据表明GPU上滤波效率不如在CPU滤波效率，而且数据越大对比越明显，下一步将探索这些问题产生的原因，并进一步改进GPU-FFT算法。
As graphics processing unit (GPU) has been developing rapidly recently with a speed over Moor's law, various applications about computer graphics have grown greatly. At the same time, the highly processing power, parallelism and programmability available nowadays on the current GPU make the general-purpose computation available.
There are many applications about general-purpose computation on GPU in CT. In this paper, we make simulations of the three-dimensional CT data using the technique of general-purpose computation on GPU. Comparing to the conventional methods, efficiency of data simulation from our method highly advances. Then we made the parallel fan-beam scan using the technique of general-purpose computation on GPU. Our numerical experiments show that the speed of image reconstruction is highly enhanced comparing to the conventional methods using the CPU.
In this paper, we implement the Fast Fourier Transform Algorithm (method) on GPU using the technique of general-purpose computation on GPU. Then, we apply this result to the filtering part of the filtering back-projection reconstruction algorithm.
在CT领域，GPU通用计算技术同样有很大的应用空间，越来越多的人开始研究GPU通用计算技术在CT中的应用，本文利用GPU通用计算技术实现了三维CT数据的仿真。用CPU进行三维数据的仿真，其仿真速度比较慢，而且模型越复杂所花费的时间越多。由于图像的渲染过程与CT的数据扫描过程很相似，受此启发，本文把CT数据扫描的过程看作图像渲染的过程，利用GPU通用计算技术在GPU上实现了CT数据仿真。实验数据表明用GPU进行数据仿真与传统的CPU进行CT数据的仿真效率得到大大提升。同样道理把CT重建的过程可以看作投影的反过程，受此启发，本文利用GPU通用计算技术实现了平行扇束CT图像重建，其中投影数据是256~*256，360个角度投影，重建体大小是256~*256~*256，测试结果表明GPU上重建时间比CPU下重建时间快了4倍左右。
本文还利用GPU通用计算技术实现了快速傅立叶变换并将结果应用到CT滤波反投影重建算法中，将滤波反投影算法统一在GPU进行。实验数据表明GPU上滤波效率不如在CPU滤波效率，而且数据越大对比越明显，下一步将探索这些问题产生的原因，并进一步改进GPU-FFT算法。
As graphics processing unit (GPU) has been developing rapidly recently with a speed over Moor's law, various applications about computer graphics have grown greatly. At the same time, the highly processing power, parallelism and programmability available nowadays on the current GPU make the general-purpose computation available.
There are many applications about general-purpose computation on GPU in CT. In this paper, we make simulations of the three-dimensional CT data using the technique of general-purpose computation on GPU. Comparing to the conventional methods, efficiency of data simulation from our method highly advances. Then we made the parallel fan-beam scan using the technique of general-purpose computation on GPU. Our numerical experiments show that the speed of image reconstruction is highly enhanced comparing to the conventional methods using the CPU.
In this paper, we implement the Fast Fourier Transform Algorithm (method) on GPU using the technique of general-purpose computation on GPU. Then, we apply this result to the filtering part of the filtering back-projection reconstruction algorithm.
引文
[1] Nathan A. Carr, Jesse D. Hall, and John C. Hart. The Ray Engine [A]. In Proceedings of Graphics Hardware, Saarbrucken, 2002. 37～46.
[2] Timothy J. Purcell, Ian Buck, William R. Mark, and Pat Hanrahan. Ray Tracing on Programmable Graphics Hardware[J]. ACM Transactions on Graphics(Proceedings of SIGGRAPH), Volume 21, Issue 3, 2002. 703～712.
[3] Naga Govindaraju, Stephane Redon, Ming C. Lin and Dinesh Manocha. CULLIDE: Interactive Collision Detection Between Complex Models in Large Environments Using Graphics Hardware[A]. In Proceedings of Graphics Hardware, San Diego, 2003. 25～32.
[4] Naga Govindaraju, Avneesh Sud, Sung-Eui Yoon and Dinesh Manocha. Parallel Occlusion Culling for Interactive Walkthroughs using Multiple GPUs[R]. UNC Computer Science Technical Report TR02-027, 2002. The University of North Carolina at Chapel Hill. Carolina.
[5] E. Scott Larsen, and David McAllister. Fast Matrix Multiplies using Graphics Hardware[A]. In Proceedings of Supercomputing, Denver, 2001. 55～60.
[6] Jesse D. Hall, Nathan A. Carr and John C. Hart. Cache and Bandwidth Aware Matrix Multiplication on the GPU[R]. UIUCDCS-R-2003-2328, April 2003. University of Illinois at Urbana-Champaign. Champaign.
[7] Chris J. Thompson, Sahngyun Hahn and Mark Oskin. Using Modern Graphics Architectures for General-Purpose Computing: A Framework and Analysis[A]. In Proceedings of International Symposium on Microarchitecture, Istanbul, 2002. 306～317.
[8] Jeff Bolz, Ian Farmer, Eitan Grinspun and Peter Schr(o|¨)oder. Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid[J]. ACM Transactions on Graphics (Proceedings of SIGGRAPH), Volume 22 , Issue 3, 2003. 917～924.
[9] Nolan Goodnight, Cliff Woolley, David Luebke and Greg Humphreys. A Multigrid Solver for Boundary Value Problems Using Programmable Graphics Hardware[A]. In Proceedings of Graphics Hardware, San Diego, 2O03. 102～111.
[10] Jens KrUger and Rudiger Westermann. Linear Algebra Operators for GPU Implementation of Numerical Algorithms[J]. ACM Transactions on Graphics(Proceedings of SIGGRAPH), Volume 22, Issue 3, 2003. 908～916.
[11] Karl E. Hillesland, Sergey Molinov, and Radek Grzeszczuk. Nonlinear Optimization Framework for Image-Based Modeling on Programmable Graphics Hardware[J]. ACM Transactions on Graphics (Proceedings of SIGBRAPH), Volume 22, Issue 3, 2003. 925～934.
[12] James H. Clark, The Geometry Engine: A VLSI Geometry System for Graphics[A], In Proceedings of SIGGRAPH, Boston, 1982. 127～133.
[13] 王少荣 孙晓鹏 刘丽艳 刁麓弘 李华．基于图形处理器的通用计算技术．信息技术快报第3卷第1期．
[14] 超级计算通讯Vol4，No．2，2006．6
[15] 吴恩华，柳有权．基于图形处理器(GPU)的通用计算
[16] http://developer.nvidia.com/
[17] http://www.ati.com/developer/
[18] Brian Cabral, Rancy Cam, and Jim Foran. Accelerated volume rendering and tomographic reconstruction using texture mapping hardware[C]. In Proceedings of IEEE Symposium on Volume Visualization 1994, pages 91～98.
[19] Klaus Mueller and Roni Yagel. Rapid 3-D Cone-Beam Reconstruction with the Simultaneous Algebraic Reconstruction Technique (SART) Using 2-D Texture Mapping Hardware[J]. IEEE Transactions on Medical imaging, 2000, VOL. 19, NO. 12.
[20] Fang Xu and Klaul Mueller. Real-time 3D computed tomographic
reconstruction using commodity graphics hardware
[2] Timothy J. Purcell, Ian Buck, William R. Mark, and Pat Hanrahan. Ray Tracing on Programmable Graphics Hardware[J]. ACM Transactions on Graphics(Proceedings of SIGGRAPH), Volume 21, Issue 3, 2002. 703～712.
[3] Naga Govindaraju, Stephane Redon, Ming C. Lin and Dinesh Manocha. CULLIDE: Interactive Collision Detection Between Complex Models in Large Environments Using Graphics Hardware[A]. In Proceedings of Graphics Hardware, San Diego, 2003. 25～32.
[4] Naga Govindaraju, Avneesh Sud, Sung-Eui Yoon and Dinesh Manocha. Parallel Occlusion Culling for Interactive Walkthroughs using Multiple GPUs[R]. UNC Computer Science Technical Report TR02-027, 2002. The University of North Carolina at Chapel Hill. Carolina.
[5] E. Scott Larsen, and David McAllister. Fast Matrix Multiplies using Graphics Hardware[A]. In Proceedings of Supercomputing, Denver, 2001. 55～60.
[6] Jesse D. Hall, Nathan A. Carr and John C. Hart. Cache and Bandwidth Aware Matrix Multiplication on the GPU[R]. UIUCDCS-R-2003-2328, April 2003. University of Illinois at Urbana-Champaign. Champaign.
[7] Chris J. Thompson, Sahngyun Hahn and Mark Oskin. Using Modern Graphics Architectures for General-Purpose Computing: A Framework and Analysis[A]. In Proceedings of International Symposium on Microarchitecture, Istanbul, 2002. 306～317.
[8] Jeff Bolz, Ian Farmer, Eitan Grinspun and Peter Schr(o|¨)oder. Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid[J]. ACM Transactions on Graphics (Proceedings of SIGGRAPH), Volume 22 , Issue 3, 2003. 917～924.
[9] Nolan Goodnight, Cliff Woolley, David Luebke and Greg Humphreys. A Multigrid Solver for Boundary Value Problems Using Programmable Graphics Hardware[A]. In Proceedings of Graphics Hardware, San Diego, 2O03. 102～111.
[10] Jens KrUger and Rudiger Westermann. Linear Algebra Operators for GPU Implementation of Numerical Algorithms[J]. ACM Transactions on Graphics(Proceedings of SIGGRAPH), Volume 22, Issue 3, 2003. 908～916.
[11] Karl E. Hillesland, Sergey Molinov, and Radek Grzeszczuk. Nonlinear Optimization Framework for Image-Based Modeling on Programmable Graphics Hardware[J]. ACM Transactions on Graphics (Proceedings of SIGBRAPH), Volume 22, Issue 3, 2003. 925～934.
[12] James H. Clark, The Geometry Engine: A VLSI Geometry System for Graphics[A], In Proceedings of SIGGRAPH, Boston, 1982. 127～133.
[13] 王少荣 孙晓鹏 刘丽艳 刁麓弘 李华．基于图形处理器的通用计算技术．信息技术快报第3卷第1期．
[14] 超级计算通讯Vol4，No．2，2006．6
[15] 吴恩华，柳有权．基于图形处理器(GPU)的通用计算
[16] http://developer.nvidia.com/
[17] http://www.ati.com/developer/
[18] Brian Cabral, Rancy Cam, and Jim Foran. Accelerated volume rendering and tomographic reconstruction using texture mapping hardware[C]. In Proceedings of IEEE Symposium on Volume Visualization 1994, pages 91～98.
[19] Klaus Mueller and Roni Yagel. Rapid 3-D Cone-Beam Reconstruction with the Simultaneous Algebraic Reconstruction Technique (SART) Using 2-D Texture Mapping Hardware[J]. IEEE Transactions on Medical imaging, 2000, VOL. 19, NO. 12.
[20] Fang Xu and Klaul Mueller. Real-time 3D computed tomographic
reconstruction using commodity graphics hardware