三维CT算法及重建质量研究
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摘要
锥束三维CT以其一次扫描就能获得被测物体整个二维投影的优势，已成为当今国际上CT领域中最活跃的前沿研究课题之一。本文对精确三维重建理论进行了分析和归纳总结，对一些抽象的定理或结论做了直观解释。精确重建的源点轨迹不在同一平面上且有大量的冗余数据，这样就增加了扫描系统的复杂性并降低了重建速度。所以重点分析了几种源点轨迹为单圆周的实用锥束重建方法即Feldkamp算法、交叉卷积法和锥形卷积法。且对实际投影数据用这三种方法进行图像重建，对这三种方法的重建结果进行比较、分析和评价得到一些有益的结论。
Because a full 2D projection data of 3D object is gotten by scanning only one time, cone-beam 3D CT has become one of the most active parts in the recent international CT research. The exact reconstruction theories have been analyzed and summarized, some abstract theories and formulas also have been straightly explained in the paper. The source position not encompassed in a plane is indispensable to the exact reconstruction and the data redundancy is produced in the exact reconstruction, thus the complexity of the scanning system is increased and the speed of reconstruction is decreased. A few practical cone-beam reconstruction algorithms, including Feldkamp, cross-convolution method and cone-convolution method are analyzed. Some useful conclusion is drawn by comparing and evaluating the reconstruction result which comes from actual projection data.
Because a full 2D projection data of 3D object is gotten by scanning only one time, cone-beam 3D CT has become one of the most active parts in the recent international CT research. The exact reconstruction theories have been analyzed and summarized, some abstract theories and formulas also have been straightly explained in the paper. The source position not encompassed in a plane is indispensable to the exact reconstruction and the data redundancy is produced in the exact reconstruction, thus the complexity of the scanning system is increased and the speed of reconstruction is decreased. A few practical cone-beam reconstruction algorithms, including Feldkamp, cross-convolution method and cone-convolution method are analyzed. Some useful conclusion is drawn by comparing and evaluating the reconstruction result which comes from actual projection data.
引文
[1] Tonner Pahl.D, Stanley..J.H., Mater Eval, 1992; 1434-1438
[2] Takahiro KANAMORI, ShouJI KAMATA, Cross-sectional imaging of large and dense materials by high energy X-ray CT using linear accelerator, Journal of Nuclear Science and Technology, 26(9), September, 1989
[3] 郭志平，董宇峰，张朝宗 工业CT技术：工业CT技术发展概况 无损检测 1996．1
[4] L.A.Feldkamp, L. C. Davis, J. W. Kress. Practical Cone-beam Algorithm, J. Opt. Soc. Am. A, 1984, 1(6):612～619
[5] HEANG K.TUY, An Inversion Formula For Cone-beam Reconstruction. SIAM J. AppL Math., 1983, 43(3):546～552
[6] G. Herman. Image Reconstruction From Projection: The Fundamentals of Computed Tomography. New York: Academic Press, 1980
[7] B.D.Smith. Image Reconstruction from Cone-Beam Projections:Necessary and Sufficient Conditions and Reconstruction Methods.IEEE Transactions on medical imaging,vol. 4,pp14-25,1985.
[8] B.D.Smith. Cone-beam tomography:recent advances and tutorial review. Optical Engineering,vol. 29,pp524-534,1990.
[9] B.D.Smith, J. Chen, Implementation,Inverstigation,and Improvement of a Novel Cone-Beam Reconstruction Method. IEEE Transactions on medical imaging, vol. 11,pp260-266,1992..
[10] Kak A C,Slaney M. Principles of Computerized Tomography Imaging.IEEE Press, 1987
[11] J.Radon,Math.Phys,PP262-277,1917
[12] Grangeate P. Mathematical framework of cone beam 3D reconstruction via the first derivate of the Radon transform. Mathematic Methods in Tomography,G. T. Herman, A. K. Louis, E Natterer(eds.), Lecture notes in Mathematics, Springer Verlag 1991
[13] Grangeat P, Mathmatical framework of cone beam 3D reconstruction via the first derivative of the Radon transform. Mathematical Methods in Tomography. G.T. Herman,A.K.Louis,F.Natterer(eds.),Lecture notes in Mathematics, Springer Verlag
1991
[14] Grangeat P, Mason P L, Melennec P, et al. Evalution of the 3D Radon transform algorithm for cone-beam reconstruction. SPIE Medical Imaging V, Technical Conference 1445: Image Processing, San Jose, California, pp. 320-331, Feb. 23-Mars 1, 1991
[15] Defrise M, Clack R. A cone-beam reconstruction by the use of Radon Transform intermediate functions algorithm using shift-invariant filtering and cone-beam backprojection. IEEE Transactions on Medical Imaging,1994,13(1): 186-195
[16] Clack R, Defrise M. Cone-beam reconstruction by the use of Radon transform intermediate functions. Journal of Optical Soc. Am. A, 1994
[17] Kudo H, Saito T. Derivation and implementation of a cone-beam reconstruction algorithm for non-planar orbits. IEEE Transaction on Medical Imaging, 1994, 13(1): 186-195
[18] Kudo H, Saito T. Feasible cone beam scanning methods for extract reconstruction in three-dimensional tomography. Journal of Optical Soc.Am.A, 1990, 7(12): 2169-2183
[19] Kudo H, Saito T. Exact Cone-Beam Reconstruction with a New Competeness Condition. Proc.of the 1995 International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Aix-les-Bains, France, pp.255-259, July 4-6, 1995
[20] Jacobson C. Direct Fourier Methods in 3D-Reconstruction from Cone-Beam Data: [Thesis]. Sweden: Department of Electrical Engineering Linkoping University, 1994
[21] Jacobson C, Danielsson P E. 3D Reconstruction from Cone-Beam Data in O(N~3 log N)time. Physics in Medicine and Biology, 1994, 39:477-491
[22] Magnusson M. Linogram and Other Direct Fourier Methods for Tomographic Reconstruction: [Dissertation]. Sweden: Department of Electrical Engineering Linkoping University, 1993
[23] 毛希平，三维锥束CT精确图象重建的理论与方法研究，清华大学博士论文，1997．
[24] 庄天戈，CT原理与算法，上海交通大学出版社，1992
[25] 庞彦伟，工业CT技术研究—提高CT图像质量的几个途径。华北工学院硕士论文．pp29-37．2001．
[26] 杨民，与转轴任意相交角下的CT改进算法——预处理、校正与滤波卷积反投影．华北工学院硕士论文．pp29-37．2000．
[27] 张羽中．锥束投影三维CT图象重建方法研究．[博士论文]．北京：清华大学，1991
[28] 高得琦，锥形束卷积三维CT图象重建方法的实现与实物分析研究，清华大学硕士论文，pp14-15．
[29] 王召巴，基于面阵CCD相机的高能X射线工业CT技术研究，南京理工大学博士学位论文，pp34-41．
[2] Takahiro KANAMORI, ShouJI KAMATA, Cross-sectional imaging of large and dense materials by high energy X-ray CT using linear accelerator, Journal of Nuclear Science and Technology, 26(9), September, 1989
[3] 郭志平，董宇峰，张朝宗 工业CT技术：工业CT技术发展概况 无损检测 1996．1
[4] L.A.Feldkamp, L. C. Davis, J. W. Kress. Practical Cone-beam Algorithm, J. Opt. Soc. Am. A, 1984, 1(6):612～619
[5] HEANG K.TUY, An Inversion Formula For Cone-beam Reconstruction. SIAM J. AppL Math., 1983, 43(3):546～552
[6] G. Herman. Image Reconstruction From Projection: The Fundamentals of Computed Tomography. New York: Academic Press, 1980
[7] B.D.Smith. Image Reconstruction from Cone-Beam Projections:Necessary and Sufficient Conditions and Reconstruction Methods.IEEE Transactions on medical imaging,vol. 4,pp14-25,1985.
[8] B.D.Smith. Cone-beam tomography:recent advances and tutorial review. Optical Engineering,vol. 29,pp524-534,1990.
[9] B.D.Smith, J. Chen, Implementation,Inverstigation,and Improvement of a Novel Cone-Beam Reconstruction Method. IEEE Transactions on medical imaging, vol. 11,pp260-266,1992..
[10] Kak A C,Slaney M. Principles of Computerized Tomography Imaging.IEEE Press, 1987
[11] J.Radon,Math.Phys,PP262-277,1917
[12] Grangeate P. Mathematical framework of cone beam 3D reconstruction via the first derivate of the Radon transform. Mathematic Methods in Tomography,G. T. Herman, A. K. Louis, E Natterer(eds.), Lecture notes in Mathematics, Springer Verlag 1991
[13] Grangeat P, Mathmatical framework of cone beam 3D reconstruction via the first derivative of the Radon transform. Mathematical Methods in Tomography. G.T. Herman,A.K.Louis,F.Natterer(eds.),Lecture notes in Mathematics, Springer Verlag
1991
[14] Grangeat P, Mason P L, Melennec P, et al. Evalution of the 3D Radon transform algorithm for cone-beam reconstruction. SPIE Medical Imaging V, Technical Conference 1445: Image Processing, San Jose, California, pp. 320-331, Feb. 23-Mars 1, 1991
[15] Defrise M, Clack R. A cone-beam reconstruction by the use of Radon Transform intermediate functions algorithm using shift-invariant filtering and cone-beam backprojection. IEEE Transactions on Medical Imaging,1994,13(1): 186-195
[16] Clack R, Defrise M. Cone-beam reconstruction by the use of Radon transform intermediate functions. Journal of Optical Soc. Am. A, 1994
[17] Kudo H, Saito T. Derivation and implementation of a cone-beam reconstruction algorithm for non-planar orbits. IEEE Transaction on Medical Imaging, 1994, 13(1): 186-195
[18] Kudo H, Saito T. Feasible cone beam scanning methods for extract reconstruction in three-dimensional tomography. Journal of Optical Soc.Am.A, 1990, 7(12): 2169-2183
[19] Kudo H, Saito T. Exact Cone-Beam Reconstruction with a New Competeness Condition. Proc.of the 1995 International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Aix-les-Bains, France, pp.255-259, July 4-6, 1995
[20] Jacobson C. Direct Fourier Methods in 3D-Reconstruction from Cone-Beam Data: [Thesis]. Sweden: Department of Electrical Engineering Linkoping University, 1994
[21] Jacobson C, Danielsson P E. 3D Reconstruction from Cone-Beam Data in O(N~3 log N)time. Physics in Medicine and Biology, 1994, 39:477-491
[22] Magnusson M. Linogram and Other Direct Fourier Methods for Tomographic Reconstruction: [Dissertation]. Sweden: Department of Electrical Engineering Linkoping University, 1993
[23] 毛希平，三维锥束CT精确图象重建的理论与方法研究，清华大学博士论文，1997．
[24] 庄天戈，CT原理与算法，上海交通大学出版社，1992
[25] 庞彦伟，工业CT技术研究—提高CT图像质量的几个途径。华北工学院硕士论文．pp29-37．2001．
[26] 杨民，与转轴任意相交角下的CT改进算法——预处理、校正与滤波卷积反投影．华北工学院硕士论文．pp29-37．2000．
[27] 张羽中．锥束投影三维CT图象重建方法研究．[博士论文]．北京：清华大学，1991
[28] 高得琦，锥形束卷积三维CT图象重建方法的实现与实物分析研究，清华大学硕士论文，pp14-15．
[29] 王召巴，基于面阵CCD相机的高能X射线工业CT技术研究，南京理工大学博士学位论文，pp34-41．