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全覆盖圆轨迹扫描的成像视野受探测器宽度限制, 对于大物体的成像效率较低.半覆盖扫描可以将成像视野扩展近1倍, 图像重建首推使用反投影滤波型算法. 反投影滤波型算法按PI线重建, 各PI线积分区间的不一致性导致通信和计算消耗大, 影响重建效率. 针对半覆盖成像中扁平形状物体的重建问题, 提出了一种改进的反投影滤波型算法, 且证明了当扁平物体的厚度小于2Rsin(2π/Np) (R为扫描半径, Np 为圆扫描一周均匀采集的投影数量)时, PI线积分区间的不一致性在数值计算过程中的误差是可以忽略的. 改进后的算法相比原半覆盖反投影滤波算法具有两个明显的优势: 一是数值计算过程中角度循环移至PI线循环之外, 算法的通信需求显著降低; 二是投影数据求导、反投影和沿PI线滤波三个步骤均能够并行计算, 算法的并行性得到增强.数值仿真与实际数据的实验结果表明, 本文算法与原半覆盖反投影滤波算法的重建精度相当, 但计算效率提高了4.6倍.In circular full-cover cone-beam computed tomography (CT), the field-of-view (FOV) is limited by the width of planar detector, resulting in low imaging efficiency for large object. The FOV can be doubled by half-cover scanning, in which the back-projection filtration (BPF) algorithm based on the concept of PI-line is the best choice for image reconstruction. However, the integral intervals of different PI-lines are unequal in the BPF algorithm, leading to heavy communication consuming and calculation. As a result, the reconstruction efficiency by use of the BPF algorithm is low. In this paper, an efficient image reconstruction strategy based on the BPF algorithm for flat object is proposed. With the method, we demonstrate that the inequality of integral interval of PI-line can be ignored in the discrete implementation of the BPF algorithm when the thickness of flat object is less than 2Rsin(2π/Np) (R is the scanning radius and Np is the number of uniform sampled projections in a full circle). Compared with the original BPF algorithm for half-cover scanning, our method has two major advantages: the first one is that the outer loop is the sample angle while the inner loop is the PI-line, which reduces the communication consuming for computer significantly; the second one is that the derivative of projection, back-projection and inverse Hilbert transform along the PI-line can be computed using parallel computing techniques readily. The results of numerical simulation and real data experiment indicate that the computational efficiency of the proposed method is 5.6 times that for original BPF algorithm and the reconstruction errors of the two methods are comparable.
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Keywords:
- cone-beam CT /
- half-cover scanning /
- back-projection filtration /
- PI-line
[1] Katsevich A 2003 Int. J. Math. 21 1305
[2] Zou Y, Pan X, Sidky E Y 2005 J. Opt. Soc. Am. A 22 2732
[3] Yu H Y, Ye Y B, Wang G 2008 J. X-ray Sci. Technol. 16 243
[4] Zeng L, Liu B D, Liu L H, Xiang C B 2010 J. X-ray Sci. Technol. 18 266
[5] Wang X C, Yan B, Li L, Hu G E 2012 Chin. Phys. B 21 118702
[6] Wang X C, Hu G E, Yan B, Han Y, Li L, Bao S L 2013 IEEE Trans. Nucl. Sci. 60 174
[7] Xu Q, Yu H Y, Mou X Q, Zhang L 2012 IEEE Trans. Med. Imaging 31 1682
[8] Zou X B, Zeng L, Li Z J 2009 J. X-ray Sci. Technol.17 233
[9] Han Y, Yan B, Li L, Yu C Q, Li J X, Bao S L 2012 Chin. Phys. B 21 068701
[10] Jia P X, Zhang F, Yan B, Bao S L 2010 Chin. Phys. B 19 087802
[11] Wang G 2002 Med. Phys. 29 1634
[12] Zou Y, Pan X C, Sidky E Y 2005 Phys. Med. Biol. 50 13
[13] Li L, Chen Z Q, Zhang L, Xing Y X, Kang K J 2007 Appl. Radiat. Isot. 65 1041
[14] Guo J Q, Zeng L, Zou X B 2011 J. X-ray Sci. Technol. 19 293
[15] Danielsson P E, Edholm P, Seger M 1997 International Meeting On Fully Three-dimensional Image Reconstruction in Radiology and Nuclear Medicine Pennsylvania, USA, June 25-28, 1997 p141
[16] Wang X C, Li L, Yu C Q, Yan B, Bao S L 2012 J. X-ray Sci. Technol. 20 69
[17] Pan X C, Xia D, Zou Y Yu L F 2004 Phys. Med. Biol. 49 4349
[18] Yu L F, Zou Y, Sidky E Y, Pelizzari C A, Munro P, Pan X C 2006 IEEE Trans. Med. Imaging 25 869
[19] Tuy H K 1983 SIAM J. Appl. Math. 43 546
[20] Kuen H T, Wayne L 2010 Proceedings of the 18th Annual ACM/SIGDA International Symposium on Field Programmable Gate Arrays New York, USA, February 20-27, 2010 p115
[21] Zhang F, Lu L Z, Li Q L, Yan B, Li L 2012 2nd World Congress on Computer Science and Information Engineering Changchun, China, June 17-19, 2012 p687
[22] Peter T 1996 Ph. D. Dissertation (Lyngby: Technical University of Denmark)
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[1] Katsevich A 2003 Int. J. Math. 21 1305
[2] Zou Y, Pan X, Sidky E Y 2005 J. Opt. Soc. Am. A 22 2732
[3] Yu H Y, Ye Y B, Wang G 2008 J. X-ray Sci. Technol. 16 243
[4] Zeng L, Liu B D, Liu L H, Xiang C B 2010 J. X-ray Sci. Technol. 18 266
[5] Wang X C, Yan B, Li L, Hu G E 2012 Chin. Phys. B 21 118702
[6] Wang X C, Hu G E, Yan B, Han Y, Li L, Bao S L 2013 IEEE Trans. Nucl. Sci. 60 174
[7] Xu Q, Yu H Y, Mou X Q, Zhang L 2012 IEEE Trans. Med. Imaging 31 1682
[8] Zou X B, Zeng L, Li Z J 2009 J. X-ray Sci. Technol.17 233
[9] Han Y, Yan B, Li L, Yu C Q, Li J X, Bao S L 2012 Chin. Phys. B 21 068701
[10] Jia P X, Zhang F, Yan B, Bao S L 2010 Chin. Phys. B 19 087802
[11] Wang G 2002 Med. Phys. 29 1634
[12] Zou Y, Pan X C, Sidky E Y 2005 Phys. Med. Biol. 50 13
[13] Li L, Chen Z Q, Zhang L, Xing Y X, Kang K J 2007 Appl. Radiat. Isot. 65 1041
[14] Guo J Q, Zeng L, Zou X B 2011 J. X-ray Sci. Technol. 19 293
[15] Danielsson P E, Edholm P, Seger M 1997 International Meeting On Fully Three-dimensional Image Reconstruction in Radiology and Nuclear Medicine Pennsylvania, USA, June 25-28, 1997 p141
[16] Wang X C, Li L, Yu C Q, Yan B, Bao S L 2012 J. X-ray Sci. Technol. 20 69
[17] Pan X C, Xia D, Zou Y Yu L F 2004 Phys. Med. Biol. 49 4349
[18] Yu L F, Zou Y, Sidky E Y, Pelizzari C A, Munro P, Pan X C 2006 IEEE Trans. Med. Imaging 25 869
[19] Tuy H K 1983 SIAM J. Appl. Math. 43 546
[20] Kuen H T, Wayne L 2010 Proceedings of the 18th Annual ACM/SIGDA International Symposium on Field Programmable Gate Arrays New York, USA, February 20-27, 2010 p115
[21] Zhang F, Lu L Z, Li Q L, Yan B, Li L 2012 2nd World Congress on Computer Science and Information Engineering Changchun, China, June 17-19, 2012 p687
[22] Peter T 1996 Ph. D. Dissertation (Lyngby: Technical University of Denmark)
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