选择性重排FDK算法及其GPU加速优化
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摘要
FDK算法是目前三维图像重建的主流算法,但是传统重排FDK算法存在占用内存量较大、重建效率不高的问题,本文提出一种选择性重排FDK算法。根据重排前后投影数据的结构关系,计算出一轮重排所加载的最少锥形束投影,并使用循环队列对有限帧数的投影进行选择性加载,显著降低了重建对内存的消耗。此外,利用新算法较好的并行性,借助图形处理单元(GPU)对算法进行了硬件加速,大大提升算法的执行效率。为验证算法有效性,对5123规模的仿真数据和实际数据进行重建,在不损失重建精度的前提下,新算法占用内存约为传统算法的1/3或1/5。本文算法对传统重排FDK算法进行了改进,有效降低了计算机内存占用,较好地解决了大规模投影数据重建问题。
FDK algorithm is widely used in computed tomography. However, the traditional rebin FDK algorithm heavily consumes memories, thus the reconstruction efficiency is low. Aiming to solve the problem, a selective projection-rebin FDK algorithm is proposed in this paper. By analyzing the geometrical relationship between the original projections and rebined ones, the least amount of cone-beam projections during each round of data rearrangement is derived. Circular queue is used to selectively load certain frames of cone-beam projections, which substantially reduces the memory-consumption. Based on graphic processing unit, the new algorithm is optimized for its parallelism performance, and the speed of the parallel method is boosted significantly. Experiments for the reconstruction of 5123 are performed to verify the effectiveness of the algorithm. Without loss of reconstruction accuracy, its memory consumption is reduced to 1/3 and 1/5 of the traditional for simulation data and real data respectively. The new algorithm, reducing the memory-consumption substantially, is the development of traditional rebin FDK algorithm, and it solves the problem of reconstruction for mass projections.
FDK algorithm is widely used in computed tomography. However, the traditional rebin FDK algorithm heavily consumes memories, thus the reconstruction efficiency is low. Aiming to solve the problem, a selective projection-rebin FDK algorithm is proposed in this paper. By analyzing the geometrical relationship between the original projections and rebined ones, the least amount of cone-beam projections during each round of data rearrangement is derived. Circular queue is used to selectively load certain frames of cone-beam projections, which substantially reduces the memory-consumption. Based on graphic processing unit, the new algorithm is optimized for its parallelism performance, and the speed of the parallel method is boosted significantly. Experiments for the reconstruction of 5123 are performed to verify the effectiveness of the algorithm. Without loss of reconstruction accuracy, its memory consumption is reduced to 1/3 and 1/5 of the traditional for simulation data and real data respectively. The new algorithm, reducing the memory-consumption substantially, is the development of traditional rebin FDK algorithm, and it solves the problem of reconstruction for mass projections.
引文
[1]Zeng GL.Medical image reconstruction[M].Beijing:Higher Education Press,2009:1-19.
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[9]Feldkamp AL,Davis LC,Kress JW.Practical cone-beam algorithm[J].Journal of the Optical Society of America A-optics Image Science and Vision,1984,(1):612-619.
[10]Wang XC,Yan B,Li L,et al.Cone-beam local reconstruction based on a radon inversion transformation[J].Chinese Physics B,2012,21(11):8702.
[11]Turbell H,Danielson PE.Fast Feldkamp reconstruction[C]//International Meeting on Fully Three-dimensional Image Reconstruction in Radiology and Nuclear Medicine,1999:311-314.
[12]Grass M,Kohler T,Proksa R.3D cone-beam CT reconstruction for circular trajectories[J].Physics in Medicine and Biology,2000,45(2):329-347.
[13]王蔚林,姜晓彤,罗立民,等.利用投影数据重排进行锥形束体积重建的改进算法[J].东南大学学报,2004,34(3):332-335.Wang WL,Jiang XT,Luo LM,et al.Improved cone-beam reconstruction algorithm with projection data rebinning[J].Journal of Southeast University,2004,34(3):332-335.(in Chinese).
[14]Han Y,Yan B,Li L,et al.Rebinned filtered back-projection reconstruction from truncated data for half-covered helical cone-beam computed tomography[J].IEEE Transactions on Nuclear Science,2014,61(5):2753-2763.
[15]Wang YJ,Hu HF,Xing YX.Strategy for GPU acceleration of massive data cone beam CT reconstruction[C]//The 10th International Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine,2009:57-60.
[2]Wang XC,Li L,Yu CQ,et al.Fast reconstruction of a flat region in a super-short scan based on MD-FBP algorithm[J].Journal of X-Ray Science and Technology,2012,20:69-77.
[3]Guo JQ,Zeng L,Liu BD.High-quality image reconstruction from exterior helical cone-beam CT data for NDE of industrial pipelines[J].Insight,2011,53(10):534-541.
[4]闫镔,韩玉,魏峰,等.锥束CT超视野成像重建算法综述[J].CT理论与应用研究,2013,22(2):373-384.Yan B,Han Y,Wei F,et al.Review of algorithms for over FOV size object in cone-beam CT[J].CT Theory and Applications,2013,22(2):373-384.(in Chinese).
[5]Jiang H.Computed tomography[M].Beijing:Science Press,2006:63-68.
[6]Pan XC,Sidky EY,Michael V.Why do commercial CT scanners still employ traditional,filtered back-projection for image reconstruction[J].Inverse Problems in Science and Engineering,2009,25(12):123009.
[7]Zhang J,Chen ZQ.Review of recent development in FDK reconstruction algorithms for 3D cone-beam CT[J].Chinese Journal of Stereology and Image Analysis,2005,10(2):116-121.
[8]Yan B,Deng L,Han Y,et al.Fast local reconstruction by selective back projection for low dose in dental computed tomography[J].Chinese Physics C,2014,38(10):108201.
[9]Feldkamp AL,Davis LC,Kress JW.Practical cone-beam algorithm[J].Journal of the Optical Society of America A-optics Image Science and Vision,1984,(1):612-619.
[10]Wang XC,Yan B,Li L,et al.Cone-beam local reconstruction based on a radon inversion transformation[J].Chinese Physics B,2012,21(11):8702.
[11]Turbell H,Danielson PE.Fast Feldkamp reconstruction[C]//International Meeting on Fully Three-dimensional Image Reconstruction in Radiology and Nuclear Medicine,1999:311-314.
[12]Grass M,Kohler T,Proksa R.3D cone-beam CT reconstruction for circular trajectories[J].Physics in Medicine and Biology,2000,45(2):329-347.
[13]王蔚林,姜晓彤,罗立民,等.利用投影数据重排进行锥形束体积重建的改进算法[J].东南大学学报,2004,34(3):332-335.Wang WL,Jiang XT,Luo LM,et al.Improved cone-beam reconstruction algorithm with projection data rebinning[J].Journal of Southeast University,2004,34(3):332-335.(in Chinese).
[14]Han Y,Yan B,Li L,et al.Rebinned filtered back-projection reconstruction from truncated data for half-covered helical cone-beam computed tomography[J].IEEE Transactions on Nuclear Science,2014,61(5):2753-2763.
[15]Wang YJ,Hu HF,Xing YX.Strategy for GPU acceleration of massive data cone beam CT reconstruction[C]//The 10th International Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine,2009:57-60.