工业CT窄角扇束卷积反投影并行图像重建研究
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摘要
能检测大型工业构件的高能X射线工业CT机对航空、军工等领域有着明显的重要性。工业CT机检测对象为大型工业构件并且要求高分辨率时，图像重建的
像素点阵巨大，计算量大大增加，从而图像重建时间过长。本论文提出用在工作站机群上的多机并行工作的并行图像重建解决高能X射线工业CT机的快速图像重建问题。
本论文介绍了工业CT和图像重建的基本理论、基本原理等有关内容，包括扫描方式和图像重建算法。采用高能直线加速器作为射线源的高能X射线工业CT机多采用窄角扇束扫描方式，其图像重建属窄角扇束扫描方式下的图像重建。本文在比较了各种算法后，采用卷积反投影算法作为并行图像重建的算法。卷积反投影算法的过程中存在并行性，其重建图像质量较好，重建速度较快，是精度与效率得到兼顾的一种算法。
本论文将窄角扇束扫描看成是多探头的平行束扫描。对于窄角扇束扫描方式，把窄角扇束重排成平行束，再由平行束卷积反投影重建算法来重建图像，是把扫描的高效率和重建方式的简便易行很好的结合起来。本论文对窄角扇束卷积反投影算法进行了并行性分析，指出把图像重建任务分解为多个子任务并行工作，并在工作站机群上讨论了窄角扇束的分解、重排、平行束卷积反投影图像重建、图像合成的并行实现。
本论文采用窄角扇束卷积反投影图像重建在工作站机群上的并行实现能解决高能X射线工业CT机的快速图像重建问题，并行图像重建的速度与参与并行实现的工作站数有关。另外基于工作站机群的高性价比、高扩展性、开发和使用上的方便灵活性等种种优点，选择工作站机群作为并行实现环境，还能降低图像重建的开发和应用成本，对提高高能X射线工业CT机的性价比具有重要意义。
High power X-ICT which can detect large industrial parts has obvious significance in the field of aviation and military affairs. When X-ICT detects large industrial parts and requires high resolving power, image reconstruction of X-ICT has huge pixel matrix and the amount of calculation increases greatly resulting in much more time of image reconstruction.This paper proposes the parallel image reconstruction based on workstations cluster to solve fast image reconstruction of high power X-ICT．
This paper presents the relevant basic theories and principles of ICT and image reconstruction, including scan mode and image reconstruction algorithm.High power X-ICT which adopts powerful beeline accelerator as radial source often uses narrow fan-beam scan mode. Its image reconstruction belongs to the image reconstruction under narrow fan-beam scan mode.After comparing different algorithms, this paper introduces convolution back projection algorithm for the parallel image reconstruction. convolution back projection algorithm has parallelism and the image reconstruction with such an algorithm has fine quality and high speed.
This paper regards narrow fan-beam scan mode as multi-detector parallel beam scan mode. The narrow fan-beams are reset into parallel beam then the image reconstruction is conducted by parallel beam' convolution back projection algorithm, which combines the high scan efficiency with the convenience of image reconstruction.This paper analyses the parallelism in narrow fan-beam' convolution back projection algorithm, divides the task of image reconstruction into several subtasks, and discusses the parallelization of narrow fan-beam' decomposition and reset, parallel beam' convolution back projection, and image accumulation.
The parallelization of image reconstruction by convolution back projection with narrow fan-beam based on workstations cluster can solve fast image reconstruction of high power X-ICT,and the speed of parallel image reconstruction relates to the numbers of workstations involved. Besides,considering the high ratio between quality and price, high scalability, the convenience and flexibility in development and utilization, selecting workstations cluster as parallelization environment can reduce the development and application cost of image reconstruction and has great significance upon increasing the ratio between quality and price of high power X-ICT.
像素点阵巨大，计算量大大增加，从而图像重建时间过长。本论文提出用在工作站机群上的多机并行工作的并行图像重建解决高能X射线工业CT机的快速图像重建问题。
本论文介绍了工业CT和图像重建的基本理论、基本原理等有关内容，包括扫描方式和图像重建算法。采用高能直线加速器作为射线源的高能X射线工业CT机多采用窄角扇束扫描方式，其图像重建属窄角扇束扫描方式下的图像重建。本文在比较了各种算法后，采用卷积反投影算法作为并行图像重建的算法。卷积反投影算法的过程中存在并行性，其重建图像质量较好，重建速度较快，是精度与效率得到兼顾的一种算法。
本论文将窄角扇束扫描看成是多探头的平行束扫描。对于窄角扇束扫描方式，把窄角扇束重排成平行束，再由平行束卷积反投影重建算法来重建图像，是把扫描的高效率和重建方式的简便易行很好的结合起来。本论文对窄角扇束卷积反投影算法进行了并行性分析，指出把图像重建任务分解为多个子任务并行工作，并在工作站机群上讨论了窄角扇束的分解、重排、平行束卷积反投影图像重建、图像合成的并行实现。
本论文采用窄角扇束卷积反投影图像重建在工作站机群上的并行实现能解决高能X射线工业CT机的快速图像重建问题，并行图像重建的速度与参与并行实现的工作站数有关。另外基于工作站机群的高性价比、高扩展性、开发和使用上的方便灵活性等种种优点，选择工作站机群作为并行实现环境，还能降低图像重建的开发和应用成本，对提高高能X射线工业CT机的性价比具有重要意义。
High power X-ICT which can detect large industrial parts has obvious significance in the field of aviation and military affairs. When X-ICT detects large industrial parts and requires high resolving power, image reconstruction of X-ICT has huge pixel matrix and the amount of calculation increases greatly resulting in much more time of image reconstruction.This paper proposes the parallel image reconstruction based on workstations cluster to solve fast image reconstruction of high power X-ICT．
This paper presents the relevant basic theories and principles of ICT and image reconstruction, including scan mode and image reconstruction algorithm.High power X-ICT which adopts powerful beeline accelerator as radial source often uses narrow fan-beam scan mode. Its image reconstruction belongs to the image reconstruction under narrow fan-beam scan mode.After comparing different algorithms, this paper introduces convolution back projection algorithm for the parallel image reconstruction. convolution back projection algorithm has parallelism and the image reconstruction with such an algorithm has fine quality and high speed.
This paper regards narrow fan-beam scan mode as multi-detector parallel beam scan mode. The narrow fan-beams are reset into parallel beam then the image reconstruction is conducted by parallel beam' convolution back projection algorithm, which combines the high scan efficiency with the convenience of image reconstruction.This paper analyses the parallelism in narrow fan-beam' convolution back projection algorithm, divides the task of image reconstruction into several subtasks, and discusses the parallelization of narrow fan-beam' decomposition and reset, parallel beam' convolution back projection, and image accumulation.
The parallelization of image reconstruction by convolution back projection with narrow fan-beam based on workstations cluster can solve fast image reconstruction of high power X-ICT,and the speed of parallel image reconstruction relates to the numbers of workstations involved. Besides,considering the high ratio between quality and price, high scalability, the convenience and flexibility in development and utilization, selecting workstations cluster as parallelization environment can reduce the development and application cost of image reconstruction and has great significance upon increasing the ratio between quality and price of high power X-ICT.
引文
[1]庄天戈．ＣＴ理论与算法[M]．上海：上海交通大学出版社，1992．
[2 ]夏建涛.断层成像技术的发展与展望.电子科技导报,1999,4: pp 12
[3]R E Alvarez and A Macovski, "Energy selective reconstruction in X ray computerized tomography ." Phys .Med.Bionl. vol.21, Feb.1976.
[4]Costello，Ian，Wells，Peter. X-ray and gamma-ray computed tomography for Industrial nondestructive testing and evaluation .Processing of SPIE-The International Society for Optical Engineering Vol.2092.1994.
[5 ]丁厚本.CT系统的评价指标.科技与数学,1990,2(3)
[6]ASTM E1570-93 standard practice for computed topographic examination
[7]Be-Shan IL. reconstruction in industrial tomography .IEEE transaction on nuclear science,1983,30(2)
[8] 王巍．工业ＣＴ窄角扇束扫描快速迭代算法研究．硕士学位论文，重庆大学，2000．
[9]R.C.冈萨雷斯 等.数字图像处理.科学出版社.1981
[10]李介谷，施鹏飞.图像处理技术.上海交通大学出版社.1990
[11]吴维聪.计算机图像处理.上海科学技术出版社.1989
[12]K T Smith.“reconstruction formulas in computerized tomography" In Proceedings Symposium on Applied Mathematical No .27.1983
[13] G.T. Herman．王洪范等译． 由投影重建图像[M]．北京：科学出版社，1985．
[14]J A Browne and G T Herman. Computerized Evaluation of Image Reconstruction Algorithms. Int J Img Syst Tech, 1996,7
[15]Chye Hwang Yan*, Robert T.Whalen , Gary S. Beauprё ，Shin Y.Yen and Sandy Napel, "Reconstruction Algorithm for CT imaging" IEEE Transaction on Medical Imaging.vol.19, No.1.Jan 2000
[16] L A Shepp Logan BF, The Fourier Reconstruction of A Head Section, IEEE Trans Nuclear Sic. NS-21(3), pp21-43, Jun 1974
[17]S W Rowland (1979), Computer Implementation of Image Reconstruction Formulas, in Image Reconstruction from Projection: Implementation and Application, pp9-80, Springer-verlag, Berlin and New York
[18]Minerbo G. MENT.A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data，Computer Graphics and Image Processing，1979，10，pp48～68
[19]庄天戈．ＣＴ理论与算法[M]．上海：上海交通大学出版社，1992．
[20]莫华，龙莉玲．X-CT图像重建的卷积反投影图解法[J]．中国医学物理学杂志，1999，16（3）：143．
[21] R C Chase，J A Stein , "an improved image algorithm for CT scanners." Med.Phys ,vol.5,
pp.497-499,Nov./Dec.1978
[22]C R Appledorn, "A new approach to the interpolation of sampled data.". IEEE Trans. Image Processing. vol. 15.369-376.1996
[23]N A Dodgson. "Quadratic interpolation for image resampling." IEEE Trans. Image Processing.
Vol.6.1322-1326.1977
[24]T M Lemann. "Survey: Interpolation Methods in Medical Image Processing.". IEEE Trans on Med Imaging.vol.18,NO.11,November 1999
[25]李海芳，X-CT卷积反投影算法内插函数的选择，太原理工大学学报，2000 31(2)
[26]E Maeland. "on the comparison of interpolation methods." IEEE Trans.Med.Imag.vol.MI-7.
pp.213-217.1988
[27]王召巴，金永．高能X射线工业ＣＴ技术的研究进展[J]．测试技术学报，2002，16（2）：79．
[28]蔡玉芳．工业ＣＴ广角扇束卷积反投影算法窗函数与内插函数研究．硕士学位论文，重庆大学，2002．
[29]周光湖.计算机断层摄影原理及应用.成都电讯工程学院出版社.1986
[30]S K Park ，R A Schowengerdt.“Image reconstruction by parametric convolution." CVGIP,vol.23. 1983
[31]A V Oppenheim. Realization of digital filters using point arithmetic. IEEE Trans.on Audio and Electronacoustics,AU-18,June,1970
[32]T Chang，G Herman. Filter Selection for the Fan Beam Convolution Algorithm, Tech. Rept. No. MIPG6, Medical Image Processing Group, Department of Computer Science, State University of New York at Buffalo, Amherst, New York，1978
[33]A C Joseph, "CT Fan Beam Reconstruction＂，IEEE Transaction on MedicalImaging.vol.11, No.1.march 1992
[34]王培容，李姣军．工业ＣＴ的数据采集方式[J]．重庆工学院学报，2002，16（3）：73．
[35]蒋阳．窄扇束角扫描ＣＴ图像系统实用化研究．硕士学位论文，重庆大学，2000．
[36]刘键.并行程序设计方法学.武汉:华中理工大学出版社,2000
[37]全惠云等.并行计算机程序设计导论.武汉:武汉大学出版社,1998
[38]梁正友.一种基于Linux工作站网络的分布并行计算的设计方法.计算机工程与应用,2001.5:pp107
[39] 陈国良.并行计算[M].北京:高等教育出版社,1999．
[40]饶文碧等.网络分布式环境下的并行计算方法.武汉工业大学学报,2000.2, vol.22(1)
[41]孙家旭等.网络并行计算与分布式编程环境.北京:科学出版社,1997
[42]张桦，吴奇．一种分布式并行处理模型的研究[J]．计算机工程，1999，25（11）：8~9．
[43]罗省贤.基于MPI的快速富里叶变换并行算法.物探化探计算技术,2000.5, vol.22(2)
[44]陈国良.并行计算[M].北京:高等教育出版社,1999．
[45]刘晓平.扇束卷积反投影法的程序优化.CT理论与应用研究,1996.2,5（1）：35
[46]汪根苗等. CT图像重建的算法优化和代码优化.CT理论与应用研究,2000,9:13
[47]张朝宗等. 用几何参数表方法实现快速重建CT图像.清华大学学报,1998, 8（7）
[48]Berkman Sahiner,Andrew E Yagle . A Fast Algorithm for Backprojection. IEEE Nuclear Science Symposium and Medical Imaging Conference ,1992,2:1169
[49]Per-Erik Danielsson. Backprojection in O(N2logN) time. IEEE Nuclear Science Symposium,1997,2:1279
[2 ]夏建涛.断层成像技术的发展与展望.电子科技导报,1999,4: pp 12
[3]R E Alvarez and A Macovski, "Energy selective reconstruction in X ray computerized tomography ." Phys .Med.Bionl. vol.21, Feb.1976.
[4]Costello，Ian，Wells，Peter. X-ray and gamma-ray computed tomography for Industrial nondestructive testing and evaluation .Processing of SPIE-The International Society for Optical Engineering Vol.2092.1994.
[5 ]丁厚本.CT系统的评价指标.科技与数学,1990,2(3)
[6]ASTM E1570-93 standard practice for computed topographic examination
[7]Be-Shan IL. reconstruction in industrial tomography .IEEE transaction on nuclear science,1983,30(2)
[8] 王巍．工业ＣＴ窄角扇束扫描快速迭代算法研究．硕士学位论文，重庆大学，2000．
[9]R.C.冈萨雷斯 等.数字图像处理.科学出版社.1981
[10]李介谷，施鹏飞.图像处理技术.上海交通大学出版社.1990
[11]吴维聪.计算机图像处理.上海科学技术出版社.1989
[12]K T Smith.“reconstruction formulas in computerized tomography" In Proceedings Symposium on Applied Mathematical No .27.1983
[13] G.T. Herman．王洪范等译． 由投影重建图像[M]．北京：科学出版社，1985．
[14]J A Browne and G T Herman. Computerized Evaluation of Image Reconstruction Algorithms. Int J Img Syst Tech, 1996,7
[15]Chye Hwang Yan*, Robert T.Whalen , Gary S. Beauprё ，Shin Y.Yen and Sandy Napel, "Reconstruction Algorithm for CT imaging" IEEE Transaction on Medical Imaging.vol.19, No.1.Jan 2000
[16] L A Shepp Logan BF, The Fourier Reconstruction of A Head Section, IEEE Trans Nuclear Sic. NS-21(3), pp21-43, Jun 1974
[17]S W Rowland (1979), Computer Implementation of Image Reconstruction Formulas, in Image Reconstruction from Projection: Implementation and Application, pp9-80, Springer-verlag, Berlin and New York
[18]Minerbo G. MENT.A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data，Computer Graphics and Image Processing，1979，10，pp48～68
[19]庄天戈．ＣＴ理论与算法[M]．上海：上海交通大学出版社，1992．
[20]莫华，龙莉玲．X-CT图像重建的卷积反投影图解法[J]．中国医学物理学杂志，1999，16（3）：143．
[21] R C Chase，J A Stein , "an improved image algorithm for CT scanners." Med.Phys ,vol.5,
pp.497-499,Nov./Dec.1978
[22]C R Appledorn, "A new approach to the interpolation of sampled data.". IEEE Trans. Image Processing. vol. 15.369-376.1996
[23]N A Dodgson. "Quadratic interpolation for image resampling." IEEE Trans. Image Processing.
Vol.6.1322-1326.1977
[24]T M Lemann. "Survey: Interpolation Methods in Medical Image Processing.". IEEE Trans on Med Imaging.vol.18,NO.11,November 1999
[25]李海芳，X-CT卷积反投影算法内插函数的选择，太原理工大学学报，2000 31(2)
[26]E Maeland. "on the comparison of interpolation methods." IEEE Trans.Med.Imag.vol.MI-7.
pp.213-217.1988
[27]王召巴，金永．高能X射线工业ＣＴ技术的研究进展[J]．测试技术学报，2002，16（2）：79．
[28]蔡玉芳．工业ＣＴ广角扇束卷积反投影算法窗函数与内插函数研究．硕士学位论文，重庆大学，2002．
[29]周光湖.计算机断层摄影原理及应用.成都电讯工程学院出版社.1986
[30]S K Park ，R A Schowengerdt.“Image reconstruction by parametric convolution." CVGIP,vol.23. 1983
[31]A V Oppenheim. Realization of digital filters using point arithmetic. IEEE Trans.on Audio and Electronacoustics,AU-18,June,1970
[32]T Chang，G Herman. Filter Selection for the Fan Beam Convolution Algorithm, Tech. Rept. No. MIPG6, Medical Image Processing Group, Department of Computer Science, State University of New York at Buffalo, Amherst, New York，1978
[33]A C Joseph, "CT Fan Beam Reconstruction＂，IEEE Transaction on MedicalImaging.vol.11, No.1.march 1992
[34]王培容，李姣军．工业ＣＴ的数据采集方式[J]．重庆工学院学报，2002，16（3）：73．
[35]蒋阳．窄扇束角扫描ＣＴ图像系统实用化研究．硕士学位论文，重庆大学，2000．
[36]刘键.并行程序设计方法学.武汉:华中理工大学出版社,2000
[37]全惠云等.并行计算机程序设计导论.武汉:武汉大学出版社,1998
[38]梁正友.一种基于Linux工作站网络的分布并行计算的设计方法.计算机工程与应用,2001.5:pp107
[39] 陈国良.并行计算[M].北京:高等教育出版社,1999．
[40]饶文碧等.网络分布式环境下的并行计算方法.武汉工业大学学报,2000.2, vol.22(1)
[41]孙家旭等.网络并行计算与分布式编程环境.北京:科学出版社,1997
[42]张桦，吴奇．一种分布式并行处理模型的研究[J]．计算机工程，1999，25（11）：8~9．
[43]罗省贤.基于MPI的快速富里叶变换并行算法.物探化探计算技术,2000.5, vol.22(2)
[44]陈国良.并行计算[M].北京:高等教育出版社,1999．
[45]刘晓平.扇束卷积反投影法的程序优化.CT理论与应用研究,1996.2,5（1）：35
[46]汪根苗等. CT图像重建的算法优化和代码优化.CT理论与应用研究,2000,9:13
[47]张朝宗等. 用几何参数表方法实现快速重建CT图像.清华大学学报,1998, 8（7）
[48]Berkman Sahiner,Andrew E Yagle . A Fast Algorithm for Backprojection. IEEE Nuclear Science Symposium and Medical Imaging Conference ,1992,2:1169
[49]Per-Erik Danielsson. Backprojection in O(N2logN) time. IEEE Nuclear Science Symposium,1997,2:1279