大视场螺旋锥束工业CT的扫描方法与重建算法研究
|
摘要
CT(Computed Tomography)是计算机层析成像的简称,它可以在不破坏被检物体的情况下得到被检物体内部的二维或三维图像,以图像的方式清晰直观地展示物体的内部结构、材质分布和缺陷。目前工业CT已应用于航空、航天、军工、铁路、汽车制造等领域,它已成为一种重要的无损检测技术。由于三维锥束CT采用高密度的面板探测器来获取投影数据,所以具有更高的射线利用率和轴向分辨率。与圆形扫描轨迹的锥束CT相比,螺旋锥束CT可以连续检测长工件,而且其扫描轨迹满足精确重建的数据完备性条件。
传统的螺旋锥束CT要求射线束在每个投影角下完全覆盖待检测区域的横截面,因此,传统螺旋锥束CT的视场区域受限于探测器尺寸。在工业CT中,有时会遇到大工件的检测,此时就需要使用大面板探测器。但是由于技术条件的限制,使得面板探测器的尺寸有限。本论文主要研究采用小面板探测器检测大工件的螺旋锥束工业CT的扫描方式及相应的重建算法,具体的研究工作有:
深入研究了视场区域半覆盖的螺旋锥束CT的扫描方式,并提出了相应的重建算法。螺旋扫描前,运载工件的转台沿平行于探测器行的方向平移一定距离,使射线源发出的射线束在每个投影角下至少覆盖待检测区域横截面的一半,然后工件绕转台的轴线旋转,同时射线源和探测器沿转台轴线的方向平移,得到半覆盖螺旋锥束CT的投影。这种半覆盖螺旋锥束CT最大可将视场直径扩大到大约2倍。
基于滤波反投影(Filtered Backprojection,FBP)的螺旋锥束FDK算法,是一种高效实用的近似重建算法。但是它要求射线束在每个投影角下完全覆盖待检测区域的横截面,且转台轴线与锥束中心射线垂直相交。针对半覆盖螺旋锥束CT中转台轴线偏离锥束中心射线的问题,提出了半覆盖螺旋锥束CT的偏心FDK算法。重建时,根据投影的位置进行加权反投影,从而得到待检测区域的重建图像。实验结果表明,当螺距较小时,该算法可以得到待检测区域的完整图像,而且由于投影数据量的减少,使重建时间约为大面板探测器传统螺旋锥束FDK算法的一半。
与先滤波再反投影的FBP算法不同,反投影滤波(Backprojection Filtration,BPF)算法是一种先将微分后的投影反投影到PI线,然后沿PI线进行Hilbert逆变换滤波的方法,可以解决横向截断投影的重建问题。由于在每个投影角下,半覆盖螺旋锥束CT的投影数据都是横向截断的,因此,本文提出了一种基于重排的半覆盖螺旋锥束CT的BPF算法。该算法首先根据重建层将半覆盖螺旋锥束投影重排为二维视场区域半覆盖的扇形束投影,然后用加权的半覆盖扇形束BPF算法重建。实验结果表明,尽管该算法需要重排投影,但是在螺距不太大的情况下,该算法可以得到待检测区域的完整图像,重建时间比偏心FDK算法更少,而且重建结果的横向截断误差较小。
对上述的半覆盖螺旋锥束CT,在每个投影角下,工件的横截面只被射线束部分覆盖。为此,提出大视场双螺旋锥束CT扫描方式。扫描时,运载工件的转台沿平行于探测器行的方向平移一定距离,然后工件绕转台的轴线旋转,同时射线源和探测器沿转台的轴线平移,得到第一次螺旋扫描的投影数据;转台带动工件沿平行于探测器行的方向再次平移一定距离,平移方向与第一次平移的方向相反,接着,工件绕转台的轴线旋转,同时射线源和探测器沿转台的轴线平移,得到第二次螺旋扫描的投影。对每次螺旋扫描而言,待检测区域的横截面在每个投影角下只被射线束部分覆盖,但是通过两次螺旋扫描,工件的横截面在每个投影角下可以被两个射线束完全覆盖。双螺旋扫描的视场直径与系统几何参数有关。在本文的实验参数中,通过双螺旋扫描,可以将视场直径扩大到1.77倍。
针对上述双螺旋锥束CT扫描方式,提出了双螺旋锥束CT的FDK型重建算法。该算法不需要重排投影数据,而且与传统的全覆盖单螺旋锥束CT的FDK算法具有同样高的计算效率。重建时,根据反投影点的位置对每个投影进行加权叠加,从而得到待检测区域的重建值。实验结果表明,在适当的螺距范围内,该算法可以获得较好的重建图像。
螺旋锥束CT的Katsevich算法是一种理论上精确的重建算法,与基于Grangeat精确重建算法相比,Katsevich算法具有较高的重建效率。本文提出了双螺旋锥束CT的Katsevich型重建算法,该算法也不需要对投影数据重排。重建时,根据得到的投影数据应用提出的双螺旋Katsevich型重建公式加权叠加,从而得到待检测区域的图像。实验结果表明,该算法受锥角、螺距和增加平移距离的影响较小,即使当螺距较大时,该算法也可以得到较好的重建图像。
为了在双螺旋CT上推广BPF算法,以进一步减少重建结果的横向截断误差。对提出的双螺旋扫描方式进行改进,并提出了双螺旋锥束的BPF型算法。该算法首先将两个螺旋的投影进行加权反投影,补全PI线上的截断数据,然后沿PI线进行Hilbert逆变换滤波。实验结果表明,该算法可以得到较好的重建效果,而且锥角、螺距和增加平移距离对提出算法的影响较小,重建结果的横向截断误差也较小。利用改进后的双螺旋扫描和BPF型算法,可以将视场直径大约扩大到两倍。
Computed tomography (CT), not damaged the inspected object, can obtain two-dimensional (2D) or three-dimensional (3D) images of the internal object. It can directly and clearly display the structure, material and defects of the inspected object with images. Industrial CT has been used in aeronautics and astronautics, military, railway, automobile manufacture, etc. It is an important non-destructive testing technology in industry. Cone-beam CT, acquired data by use of density planar detector, can be used for rapid volumetric imaging with high longitudinal resolution and for efficient utilization of x-ray source. It can obtain more than thousand images with one turn scanning. Compared to cone-beam CT with circular trajectory, helical cone-beam CT can continuously inspect long workpiece, and its trajectory satisfies the sufficient condition of complete data.
Conventional helical cone-beam CT assumes that the entire cross-section of the object is illuminated with x-rays at each view angle. The field of view (FOV) is limited by size of the planar detector. In industrial CT, large workpiece is sometimes inspected. At this time, large planar detector must be used. Unfortunately, the size of planar detector is limited by technology. This dissertation mainly studies the scan mode and reconstruction algorithm for inspecting large workpiece with helical cone-beam industrial CT and small planar detector. The main work is as follows.
This dissertation deeply analyses the half-cover scan mode of the FOV and reconstruction algorithm for helical cone-beam CT. Before helical scanning, the gantry, which carries the inspected workpiece, translates given distance along the detector row, and more than half of the cross-section of the tested object is covered by x-ray beam at each view angle. Workpiece rotates around the axis of the gantry. The source and detector translate along the axis of the gantry simultaneously. The half-cover data can be obtained. The FOV of the half-cover helical cone-beam CT can be greatest extended up to about two times.
FDK algorithm, based on filtered backprojection (FBP), is high efficient, practical and approximate algorithm. This algorithm needs the x-ray beam to cover corss-section completely at each view angle, and the center ray of cone beam intersects and is perpendicular to the axis of gantry. Because the center ray departs from the axis of gantry in half-cover helical cone-beam CT, off-center FDK algorithm is proposed. When reconstructing, data are weightedly backprojected according to the position of projection. Experimental results validate that off-center FDK algorithm of the half-cover helical cone-beam CT can get complete image of the tested object with small helical pitch, and the reconstruction time can be saved about half of the conventional FDK algorithm because of reduction of projections.
Contrary to filtered backprojection (FBP) algorithm, backprojection filtration (BPF) algorithm firstly backprojects the differential data to PI line, and then filters along PI line by use of Hilbert inverse transform. It can reconstruct object function from transversely truncated data. This dissertation proposed rebinning-based BPF algorithm for half-cover helical cone-beam CT due to the transversely truncated data at each view angle. The proposed algorithm firstly rebins the half-cover helical cone-beam data to half-cover 2D fan-beam data, and then weighted BPF algorithm is used. Experimental results validate that rebinning-based BPF algorithm can get complete image of the inspected field with less truncated artifact, and reconstruction time is less than the off-center FDK algorithm, although projections are rebinned in proposed algorithm.
The cross-section of workpiece is partly covered by x-ray at each view angle in half-cover helical cone-beam CT. Dual-helical cone-beam CT, which can scan large FOV, is proposed. When scanning, gantry and workpiece are translated given distance along detector row, which is similar to the half-cover helical cone-beam CT. Workpiece rotates around the axis of the gantry, and the x-ray source and detector are translated along axis of gantry simultaneously. After the first helical data are acquired, the workpiece is translated again along the detector row, which direction is contrary to the first one. Then the workpiece rotates, and the x-ray source and detector are translated along the axis of the gantry simultaneously. The second helical data can be obtained. Although the cross-section of inspected field is partly covered by x-ray beam at each view angle for each helical scanning, the cross-section can be completely covered by two helical scanning at each view angle. Radius of FOV of the dual-helical cone-beam CT relates to geometry parameters of system. The Radius of FOV can be extended up to 1.77 times with parameters of this dissertation.
FDK-type algorithm is proposed for dual-helical cone-beam CT, which does not rebin projections and is high efficient as same as conventional helical FDK algorithm. When reconstructing, each projection is weightedly superposed according to the backprojected position. The reconstruction image can be acquired. Computer simulations validate that good image reconstructed by FDK-type algorithm can be got with appropriate pitch, and the algorithm is low consumed. It can extend the FOV up to 1.77 times.
Katsevich algorithm is theoretically exact algorithm. Compared with Grangeat-type algorithm, Katsevich algorithm is high efficient. The dissertation proposed Katsevich-type algorithm for dual-helical cone-beam CT, which does not rebin projections, too. When reconstructing, the backprojected data are weightedly superposed according to proposed dual helical Katsevich-type algorithm. The image of the inspected filed can be obtained. Computer simulations validate that cone-angle, pitch, and increased translation distance have less impact on Katsevich-type algorithm, Although the helical pitch is large, the proposed algorithm can obtain good reconstructed images.
This dissertation improves the dual-helical scan mode and proposes dual helical BPF-type algorithm in order to reduce the transversely truncated error. The proposed algorithm firstly backprojects data along PI lines. The differential data are weightedly backprojected, which patches the missing data on the PI line. And then the Hilbert inverse transform is implemented along the PI line. Computer simulations validate that images reconstructed by BPF-type algorithm are good. Cone angle, pitch, and increased translation distance have less impact on BPF-type algorithm, too. The reconstruction images have less truncated artifacts. Furthermore, the FOV can be extended up to about two times if the BPF-type algorithm and improved dual-helical cone-beam are used.
传统的螺旋锥束CT要求射线束在每个投影角下完全覆盖待检测区域的横截面,因此,传统螺旋锥束CT的视场区域受限于探测器尺寸。在工业CT中,有时会遇到大工件的检测,此时就需要使用大面板探测器。但是由于技术条件的限制,使得面板探测器的尺寸有限。本论文主要研究采用小面板探测器检测大工件的螺旋锥束工业CT的扫描方式及相应的重建算法,具体的研究工作有:
深入研究了视场区域半覆盖的螺旋锥束CT的扫描方式,并提出了相应的重建算法。螺旋扫描前,运载工件的转台沿平行于探测器行的方向平移一定距离,使射线源发出的射线束在每个投影角下至少覆盖待检测区域横截面的一半,然后工件绕转台的轴线旋转,同时射线源和探测器沿转台轴线的方向平移,得到半覆盖螺旋锥束CT的投影。这种半覆盖螺旋锥束CT最大可将视场直径扩大到大约2倍。
基于滤波反投影(Filtered Backprojection,FBP)的螺旋锥束FDK算法,是一种高效实用的近似重建算法。但是它要求射线束在每个投影角下完全覆盖待检测区域的横截面,且转台轴线与锥束中心射线垂直相交。针对半覆盖螺旋锥束CT中转台轴线偏离锥束中心射线的问题,提出了半覆盖螺旋锥束CT的偏心FDK算法。重建时,根据投影的位置进行加权反投影,从而得到待检测区域的重建图像。实验结果表明,当螺距较小时,该算法可以得到待检测区域的完整图像,而且由于投影数据量的减少,使重建时间约为大面板探测器传统螺旋锥束FDK算法的一半。
与先滤波再反投影的FBP算法不同,反投影滤波(Backprojection Filtration,BPF)算法是一种先将微分后的投影反投影到PI线,然后沿PI线进行Hilbert逆变换滤波的方法,可以解决横向截断投影的重建问题。由于在每个投影角下,半覆盖螺旋锥束CT的投影数据都是横向截断的,因此,本文提出了一种基于重排的半覆盖螺旋锥束CT的BPF算法。该算法首先根据重建层将半覆盖螺旋锥束投影重排为二维视场区域半覆盖的扇形束投影,然后用加权的半覆盖扇形束BPF算法重建。实验结果表明,尽管该算法需要重排投影,但是在螺距不太大的情况下,该算法可以得到待检测区域的完整图像,重建时间比偏心FDK算法更少,而且重建结果的横向截断误差较小。
对上述的半覆盖螺旋锥束CT,在每个投影角下,工件的横截面只被射线束部分覆盖。为此,提出大视场双螺旋锥束CT扫描方式。扫描时,运载工件的转台沿平行于探测器行的方向平移一定距离,然后工件绕转台的轴线旋转,同时射线源和探测器沿转台的轴线平移,得到第一次螺旋扫描的投影数据;转台带动工件沿平行于探测器行的方向再次平移一定距离,平移方向与第一次平移的方向相反,接着,工件绕转台的轴线旋转,同时射线源和探测器沿转台的轴线平移,得到第二次螺旋扫描的投影。对每次螺旋扫描而言,待检测区域的横截面在每个投影角下只被射线束部分覆盖,但是通过两次螺旋扫描,工件的横截面在每个投影角下可以被两个射线束完全覆盖。双螺旋扫描的视场直径与系统几何参数有关。在本文的实验参数中,通过双螺旋扫描,可以将视场直径扩大到1.77倍。
针对上述双螺旋锥束CT扫描方式,提出了双螺旋锥束CT的FDK型重建算法。该算法不需要重排投影数据,而且与传统的全覆盖单螺旋锥束CT的FDK算法具有同样高的计算效率。重建时,根据反投影点的位置对每个投影进行加权叠加,从而得到待检测区域的重建值。实验结果表明,在适当的螺距范围内,该算法可以获得较好的重建图像。
螺旋锥束CT的Katsevich算法是一种理论上精确的重建算法,与基于Grangeat精确重建算法相比,Katsevich算法具有较高的重建效率。本文提出了双螺旋锥束CT的Katsevich型重建算法,该算法也不需要对投影数据重排。重建时,根据得到的投影数据应用提出的双螺旋Katsevich型重建公式加权叠加,从而得到待检测区域的图像。实验结果表明,该算法受锥角、螺距和增加平移距离的影响较小,即使当螺距较大时,该算法也可以得到较好的重建图像。
为了在双螺旋CT上推广BPF算法,以进一步减少重建结果的横向截断误差。对提出的双螺旋扫描方式进行改进,并提出了双螺旋锥束的BPF型算法。该算法首先将两个螺旋的投影进行加权反投影,补全PI线上的截断数据,然后沿PI线进行Hilbert逆变换滤波。实验结果表明,该算法可以得到较好的重建效果,而且锥角、螺距和增加平移距离对提出算法的影响较小,重建结果的横向截断误差也较小。利用改进后的双螺旋扫描和BPF型算法,可以将视场直径大约扩大到两倍。
Computed tomography (CT), not damaged the inspected object, can obtain two-dimensional (2D) or three-dimensional (3D) images of the internal object. It can directly and clearly display the structure, material and defects of the inspected object with images. Industrial CT has been used in aeronautics and astronautics, military, railway, automobile manufacture, etc. It is an important non-destructive testing technology in industry. Cone-beam CT, acquired data by use of density planar detector, can be used for rapid volumetric imaging with high longitudinal resolution and for efficient utilization of x-ray source. It can obtain more than thousand images with one turn scanning. Compared to cone-beam CT with circular trajectory, helical cone-beam CT can continuously inspect long workpiece, and its trajectory satisfies the sufficient condition of complete data.
Conventional helical cone-beam CT assumes that the entire cross-section of the object is illuminated with x-rays at each view angle. The field of view (FOV) is limited by size of the planar detector. In industrial CT, large workpiece is sometimes inspected. At this time, large planar detector must be used. Unfortunately, the size of planar detector is limited by technology. This dissertation mainly studies the scan mode and reconstruction algorithm for inspecting large workpiece with helical cone-beam industrial CT and small planar detector. The main work is as follows.
This dissertation deeply analyses the half-cover scan mode of the FOV and reconstruction algorithm for helical cone-beam CT. Before helical scanning, the gantry, which carries the inspected workpiece, translates given distance along the detector row, and more than half of the cross-section of the tested object is covered by x-ray beam at each view angle. Workpiece rotates around the axis of the gantry. The source and detector translate along the axis of the gantry simultaneously. The half-cover data can be obtained. The FOV of the half-cover helical cone-beam CT can be greatest extended up to about two times.
FDK algorithm, based on filtered backprojection (FBP), is high efficient, practical and approximate algorithm. This algorithm needs the x-ray beam to cover corss-section completely at each view angle, and the center ray of cone beam intersects and is perpendicular to the axis of gantry. Because the center ray departs from the axis of gantry in half-cover helical cone-beam CT, off-center FDK algorithm is proposed. When reconstructing, data are weightedly backprojected according to the position of projection. Experimental results validate that off-center FDK algorithm of the half-cover helical cone-beam CT can get complete image of the tested object with small helical pitch, and the reconstruction time can be saved about half of the conventional FDK algorithm because of reduction of projections.
Contrary to filtered backprojection (FBP) algorithm, backprojection filtration (BPF) algorithm firstly backprojects the differential data to PI line, and then filters along PI line by use of Hilbert inverse transform. It can reconstruct object function from transversely truncated data. This dissertation proposed rebinning-based BPF algorithm for half-cover helical cone-beam CT due to the transversely truncated data at each view angle. The proposed algorithm firstly rebins the half-cover helical cone-beam data to half-cover 2D fan-beam data, and then weighted BPF algorithm is used. Experimental results validate that rebinning-based BPF algorithm can get complete image of the inspected field with less truncated artifact, and reconstruction time is less than the off-center FDK algorithm, although projections are rebinned in proposed algorithm.
The cross-section of workpiece is partly covered by x-ray at each view angle in half-cover helical cone-beam CT. Dual-helical cone-beam CT, which can scan large FOV, is proposed. When scanning, gantry and workpiece are translated given distance along detector row, which is similar to the half-cover helical cone-beam CT. Workpiece rotates around the axis of the gantry, and the x-ray source and detector are translated along axis of gantry simultaneously. After the first helical data are acquired, the workpiece is translated again along the detector row, which direction is contrary to the first one. Then the workpiece rotates, and the x-ray source and detector are translated along the axis of the gantry simultaneously. The second helical data can be obtained. Although the cross-section of inspected field is partly covered by x-ray beam at each view angle for each helical scanning, the cross-section can be completely covered by two helical scanning at each view angle. Radius of FOV of the dual-helical cone-beam CT relates to geometry parameters of system. The Radius of FOV can be extended up to 1.77 times with parameters of this dissertation.
FDK-type algorithm is proposed for dual-helical cone-beam CT, which does not rebin projections and is high efficient as same as conventional helical FDK algorithm. When reconstructing, each projection is weightedly superposed according to the backprojected position. The reconstruction image can be acquired. Computer simulations validate that good image reconstructed by FDK-type algorithm can be got with appropriate pitch, and the algorithm is low consumed. It can extend the FOV up to 1.77 times.
Katsevich algorithm is theoretically exact algorithm. Compared with Grangeat-type algorithm, Katsevich algorithm is high efficient. The dissertation proposed Katsevich-type algorithm for dual-helical cone-beam CT, which does not rebin projections, too. When reconstructing, the backprojected data are weightedly superposed according to proposed dual helical Katsevich-type algorithm. The image of the inspected filed can be obtained. Computer simulations validate that cone-angle, pitch, and increased translation distance have less impact on Katsevich-type algorithm, Although the helical pitch is large, the proposed algorithm can obtain good reconstructed images.
This dissertation improves the dual-helical scan mode and proposes dual helical BPF-type algorithm in order to reduce the transversely truncated error. The proposed algorithm firstly backprojects data along PI lines. The differential data are weightedly backprojected, which patches the missing data on the PI line. And then the Hilbert inverse transform is implemented along the PI line. Computer simulations validate that images reconstructed by BPF-type algorithm are good. Cone angle, pitch, and increased translation distance have less impact on BPF-type algorithm, too. The reconstruction images have less truncated artifacts. Furthermore, the FOV can be extended up to about two times if the BPF-type algorithm and improved dual-helical cone-beam are used.
引文
[1] Jiang Hsieh. Computed tomography:principle, design, artifacts and recent advances [M].北京:科学出版社, 2006: 1-71.
[2] William H. Oldendorf. Isolated flying spot detection of radio density discontinuities-displaying the internal structural pattern of a complex object [P]. IRE Trans. 1961, BME-8, 68-72.
[3] A. M. Cormack. Representation of a function by its line integrals with some radiological applications [J]. Journal of Applied Physics, 1963, 34: 2722-2727.
[4] G T. Herman. Image reconstruction from projections: the fundamentals of computerized tomography [M]. New York: Academic Press, 1980.
[5]庄天戈. CT原理和算法[M].上海:上海交通大学出版社, 1992: 1-99.
[6] Avinash C. Kak, Malcolm Slaney. Principles of computerized tomographic imaging [M]. New York: IEEE Press, 1999.
[7] David Nahamoo, Carl R.Crawford, Avinash C Kak. Design constraints and reconstruction algorithms for traverse-continuous-rotate CT scanners [J]. IEEE Transactions on Biomedical Engineering, 1981, 28(2):79-98.
[8]叶海霞.工业CT窄角扇束卷积反投影并行图像重建研究[D].重庆:重庆大学, 2003.
[9] Crawford, R. Carl, King, F. Kevin. Computed tomography scanning with simultaneous patient translation [J]. Medical Physics, 1990, 17(6): 967-982.
[10] W. A. Kalender, W. Seissler, E. Klotz, et al. Spiral volumetric CT with single-breath-hold technique, continuous transport, and continuous scanner rotation [J]. Radiology, 1990. 176(1): 181-183.
[11] J. S. Arenson, R. Levinson, and D. Freundlich. Dual slice scanner [P]. US Patent No. 5228069, 1993.
[12] Y. Liang, R. A. Kruger. Dual-slice spiral versus single-slice spiral scanning: comparison of the physical performance of two computed tomography scanners [J]. Medical Physics, 1996.23(2): 205-220.
[13] H. Hu. Multi-slice helical CT: Scan and reconstruction [J]. Medical Physics, 1999, 26(1): 5–18.
[14] H. Hu, H. He, W. Foley, et al. Helical CT imaging performance of a new multislice scanner [C]. Proceeding of SPIE Medical Imaging, 3661, San Diego, CA, 1999, 450–461.
[15] K. Taguchi and H. Aradate. Algorithm for image reconstruction in multislice helical CT [J] Medical Physics, 1998, 25(4): 550–561.
[16] Birgit Ertl-Wagner, Lara Eftimov, Jeffrey Blume, et al. Cranial CT with 64-, 16-, 4- andsingle-slice CT systems–comparison of image quality and posterior fossa artifacts in routine brain imaging with standard protocols [J]. European Radiology, 2008, 18(8): 1720-1726.
[17] Patrick J. La Rivière, Xiaochuan Pan. Longitudinal sampling and aliasing in multi-slice helical computed tomography [C]. IEEE Transactions on Medical Imaging, 2001: 79-83.
[18] A. F. Kopp, K. Klingenbeck-Regn, M. Heuschmid, et al. Multislice computed tomography: basic principles and clinical applications [J]. Electromedica, 2000, 68(2): 94-105.
[19] Hui Hu, Tinsu Pan, and Yun Shen. Multislice helical CT: Image temporal resolution [J]. IEEE Transactions on Medical Imaging, 2000, 19(5): 384-390.
[20] L. A. Feldkamp, L. C. Davis, and J. W. Kress. Practical cone-beam algorithm [J]. Journal of Optical Society America, 1984, A 1(6): 612-619.
[21] Bruce D. Smith. Image reconstruction from cone-beam projections: Necessary and sufficient conditions and reconstruction methods [J]. IEEE Transactions on Medical Imaging, 1985, MI-4 (1): 14-25.
[22] Ge Wang, Tein-Hsiang Lin, Ping-chin Cheng, et al. A general cone-beam reconstruction algorithm [J]. IEEE Transactions on Medical Imaging, 1993, 12(3): 486-496.
[23] Ben Wang, Hong Liu, Ge Wang. Generalized Feldkamp image reconstruction from equiangular cone-beam projection data [C]. Proceedings of the 13th IEEE Symposium on Computer-Based Medical Systems, 2000.
[24] H. Kudo, T. Satio. Helical-scan computed tomography using cone-beam projections [C]. Nuclear Science Symposium and Medical Imaging Conference, 1991, 3: 1958– 1962.
[25]毛希平,康克军.三维CT图象精确重建的源点轨迹[J]. CT理论与应用研究, 1997, 6(2): 30-33.
[26] Xiaohui Wang, and Ruola Ning. A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry [J]. IEEE Transactions on Medical Imaging, 1999, 18(9): 815-824.
[27] Xiangyang Tang, and Ruola Ning. A cone beam filtered backprojection (CB-FBP) reconstruction algorithm for a circle-plus-two-arc orbit [J]. Medical Physics, 2001 28(6): 1042-55.
[28] K. C. Tam, G. Lauritsch, K. Sourbelle, et al. Exact (Spiral+Circles) scan region-of-interest cone beam reconstruction via backprojection [J]. IEEE Transaction on Medical Imaging, 2000, 19(5): 376-373.
[29]吕东辉,庄天戈,严壮志,等.体积CT精确重建的完全性条件研究[J].生物医学工程学杂志, 2002, 19(1): 80-83.
[30]牛小明.螺旋锥束工业CT的Katsevich精确重建算法研究[D].重庆:重庆大学, 2008.
[31] D. L. Parker. Optimal short scan convolution reconstruction for fan beam CT [J]. MedicalPhysics, 1982, 9, 254–257.
[32] Lifeng Yu, Xiaochuan Pan. Half-scan fan-beam computed tomography with improved noise and resolution properties [J]. Medical Physics, 2003, 30(10): 2629-2637.
[33] Hiroyuki Kudo, Frédéric Noo, Michel Defrise, et al. New super-short-scan algorithms for fan-beam and cone-beam reconstruction [C]. IEEE Nuclear Science Symposium Conference Record, 2002, 2: 902- 906
[34] Jianhua Ma, Lingjian Chen, Jing Huang, et al. An improved super-short-scan reconstruction for fan-beam computed tomography[C]. 15th IEEE International Conference on Image Processing, 2008, 2936-2939.
[35] Hengyong Yu, Ge Wang. Feldkamp-type VOI reconstruction from super-short-scan cone-beam data [J]. Medical Physics, 2004, 31(6):1357-1362.
[36] Dong Yang and Ruola Ning. FDK half-scan with a heuristic weighting scheme on a flat panel detector-based cone beam CT (FDKHSCW) [J]. International Journal of Biomedical Imaging, 2006: 1–8.
[37] Lei Zhu, and Rebecca Fahrig. Shift-invariant cone-beam FBP reconstruction on not less than a short scan [C]. IFMBE Proceedings,4(14): 2361-2365.
[38] Jicun Hu, Kwok Tam, Jinyi Qi. An approximate short scan helical FDK cone beam algorithm based on curved surfaces satisfying the Tuy's condition [J]. Medical Physics, 2005, 32(6):1529-1536.
[39] Jicun Hu, Kwok Tam, Roger H Johnson, et al. A short scan helical FDK cone beam algorithm based on surfaces satisfying the Tuy’s condition [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 5: 2760–2764.
[40] Frédéric Noo, Hiroyuki Kudo, Michel Defrise. Approximate Short-scan Filtered-backprojection for Helical CB Reconstruction [C]. IEEE Nuclear Science Symposium, 1998. Conference Record, 1998, 3: 2073-2077.
[41] Jed D Pack, Frédéric Noo, and Hiroyuki Kudo. Investigation of saddle trajectories for cardiac CT imaging in cone-beam geometry [J]. Physics in Medicine and Biology, 2004, 49: 2317–2336
[42] Hengyong Yu, Shiying Zhao, Yangbo Ye, et al. Exact BPF and FBP algorithms for nonstandard saddle curves [J]. Medical Physics, 2005, 32(11): 3305-3312.
[43] Dan Xia, Seungryong Cho, Xiaochuan Pan. Reconstructible Volume for Cone-beam CT with a Reduced Saddle Trajectory [C]. IEEE Nuclear Science Symposium Conference Record, 2007, 2630-2632.
[44] Haiquan Yang, Meihua Li, Kazuhito Koizumi, et al. View-independent reconstruction algorithms for cone beam CT with general saddle trajectory [J]. Physics in Medicine and Biology,2006, 51: 3865-3884.
[45] Dan Xia, Seungryong Cho, Xiaochuan Pan. Reconstructible volume for cone-beam CT with a reduced saddle trajectory [C]. Nuclear Science Symposium Conference Record, 2007. IEEE, 4:2630– 2632.
[46] Haiquan Yang, Meihua Li, Kazuhito Koizumi, et al. Exact cone beam reconstruction for a saddle trajectory [J]. Physics in Medicine and Biology, 2006, 51 1157-1172.
[47] Ying Liu, Hong Liu, and Ge Wang. Half-scan cone-beam CT fluoroscopy with multiple x-ray sources [J]. Medical Physics, 2001, 28(7): 166-1471.
[48] Jun Zhao, Ming Jiang, Tiange Zhuang, et al. An exact reconstruction algorithm for triple-source helical cone-beam CT [J]. Journal of X-Ray Science and Technology, 2006, 14: 191–206.
[49] Jun Zhao, Ming Jiang, Tiange Zhuang, et al. Minimum detection window and inter-helix PI-line with triple-source helical cone-beam Scanning [J]. Journal of X-Ray Science and Technology, 2006, 14: 95–107.
[50] Yang Lu, Jun Zhao, and Ge Wang. Exact image reconstruction for triple-source cone-beam CT along saddle trajectories [C]. Proceedings of the SPIE, 2008, 7078: 70780K-70780K-11.
[51] Yang Lu, Jun Zhao. Approximate algorithms for 2N+1 sources cone-beam CT along saddle trajectories [C]. 7th Asian-Pacific Conference on Medical and Biological Engineering, 2008, 19: 229–232.
[52] Jun Zhao, Yannan Jin, Yang Lu, et al. A Filtered Backprojection Algorithm for Triple-Source Helical Cone-Beam CT [J]. IEEE Transactions on Medical Imaging, 2009, 28(3): 384-393.
[53] Yang Lu, Jun Zhao and Ge Wang. Exact image reconstruction with triple-source saddle-curve cone-beam scanning [J]. Physics in Medicine and Biology, 2009, 54: 2971-2991.
[54] S. Valton, F. Peyrin, D. Sappey-Marinie. Generalization of FDK 3D tomographic reconstruction algorithm for an off-centered cone beam geometry [C]. IEEE International Conference on Image Processing, ICIP, 2005, 3: 620-623.
[55] S. Valton, F. Peyrin, D. Sappey-Marinier. A comparative study of three tomographic reconstruction methods in cone beam off-centered circular geometry [C]. 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings, 2006, 228-1231.
[56] S. Valton, F. Peyrin, and D. Sappey-Marinier. A FDK-based reconstruction method for off-centered circular trajectory cone beam tomography [J]. IEEE Transactions on Nuclear Science, 2006, 53(5): 2736-2745.
[57] Satoshi Yoshizawa, Toshiyuki Tanaka, Kazuo Kikuchi. The method of high-accuracy 3D reconstruction for oblique X-ray CT images [C]. SICE Annual Conference, 2007, Kagawa University, Japan, 2007, 146-150.
[58] Jiang Hsieh. Tomographic reconstruction for tilted helical multislice CT [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 864-872.
[59] Ming Yan, Cishen Zhang, Hongzhu Liang, et al. Gantry tilted plane Feldkamp type reconstruction algorithm [C]. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference Shanghai, China, September 1-4, 2005, pp1810-1813.
[60] Frédéric Noo, Michel Defrise, and Hiroyuki Kudo. General reconstruction theory for multislice x-ray computed tomography with a gantry tilt [J]. IEEE Transactions on Medical Imaging, 2004, 23(9): 1109-1116.
[61] Ming Yan, Cishen Zhang, and Hongzhu Liang. An approximate cone beam reconstruction algorithm for gantry-tilted CT using tangential filtering [J]. Development of Computed Tomography Algorithms, 2006.
[62] Shuai Leng, Tingliang Zhuang, Brian E. Nett, et al. Helical cone-beam computed tomography image reconstruction algorithm for a tilted gantry with N-PI data acquisition [J]. Optical Engineering, 2007, 46(1):015004-1—015004-14.
[63]王召巴,陈军.扁平构件的CT重建方法研究[J].应用基础与工程科学学报, 2001, 9(2-3): 222-227.
[64] Yangbo Ye, Shiying Zhao, Hengyong Yu, et al. Exact reconstruction for cone-beam scanning along nonstandard spirals and other curves [C]. Proceeding of SPIE, 2004, 5535: 293-300.
[65] Jiehua Zhu, Shiying Zhao, Hengyong Yu, et al. Numerical studies on Feldkamp-type and Katsevich-type algorithms for cone-beam scanning along nonstandard spirals [C]. Proceeding of SPIE, 2005, 5535: 558-565.
[66] Yangbo Ye, Shiying Zhao, Hengyong Yu, et al. A general exact reconstruction for cone-beam CT via backprojection-filtration [J]. IEEE Transactions on Medical Imaging, 2005, 24(9): 1190-1198.
[67] Hengyong Yu, Yangbo Ye, Shiying Zhao, et al. A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an N-PI Window [J]. Physics in Medicine and Biology, 2005, 50: 2099-2111.
[68] Ge Wang, Yangbo Ye, and Hengyong Yu. Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning [J]. Physics in Medicine and Biology, 2007, 52: R1–R13.
[69]莫仕林,曾理,王珏.基于Master/Slave模式的CT同时代数重建的并行进程[J].工程数学学报, 2004, 21(8): 111-115.
[70] Baodong Liu, Li Zeng, Dongjiang Ji.. Algebraic reconstruction technique class for linear scan CT of long object [C]. Proceedings of the 17th World Conference on Non-destructive Testing,2008.
[71] Baodong Liu; Li Zeng. Parallel SART algorithm of linear scan cone-beam CT for fixed pipeline [J]. Journal of X-Ray Science and Technology, 2009, 17(3): 221-232.
[72] Emil Y Sidky, and Xiaochuan Pan. Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization [J]. Physics in Medicine and Biology, 2008, 53: 4777–4807.
[73] Jiang Hsieh. A nonlinear helical reconstruction algorithm for multislice CT [J]. IEEE Transactions on Nuclear Science, 2002, 49(3): 740-744.
[74] Stefan Schaller, Thomas Flohr, Klaus Klingenbeck, et al. Spiral interpolation algorithm for multislice spiral CT—Part I: Theory [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 822-834.
[75] Theobald Fuchs, Jens Krause, Stefan Schaller, et al. Spiral Interpolation algorithms for multislice spiral CT—Part II: Measurement and evaluation of slice sensitivity profiles and noise at a clinical multislice system [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 835-847.
[76] J. Hsieh, T. Toth, P. Simoni, et al. A multi-slice helical CT reconstruction with generalized weighting [C]. Nuclear Science Symposium Conference Record, 2001 IEEE, 3: 1732-1736.
[77] Wenwu Sun, Siping Chen, Tiange Zhuang. Reconstruction algorithm with improved efficiency and flexibility in multi-slice spiral CT [C]. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, 2005, 1901-1904.
[78]曾凯,陈志强,张丽,等.基于同心圆轨道的锥形束CT重建算法[J].清华大学学报(自然科学版), 2004, 44 (6): 725-727,731.
[79]曾凯,陈志强,张丽,等.圆轨道锥束重建精度与锥角关系的研究[J]. CT理论与应用研究, 2003, 12 (3): 9-16.
[80] Henrik Turbell. Cone-beam reconstruction using filtered backprojection [D]. Link?pings universitet, Link?ping, Sweden, 2001.
[81] M Grass, Th K?hler and R Proksa. 3D cone-beam CT reconstruction for circular trajectories [J]. Physics in Medicine Biology, 2000, 45: 329-347.
[82] Turbell, H. and P.E. Danielsson. Fast Feldkamp reconstruction [C]. International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Egmond aan Zee, The Netherlands, 1999, 311–314.
[83] Frédéric Noo, Michel Defrise, and Rolf Clackdoyle. Single-slice rebinning method for helical cone-beam CT [J]. Physics in Medicine Biology, 1999, 44: 561–570.
[84] H. Bruder, M. Kachelrie?, S. Schaller, et al. Single-slice rebinning reconstruction in spiral cone-beam computed tomography [J]. IEEE Transactions on Medical Imaging, 2000,19(9):873-887.
[85] Marc Kachelrie?, Stefan Schaller, Willi A. Kalender. Advanced single-slice rebinning in cone-beam spiral CT [J]. Medical Physics, 2000, 27(4): 753-772.
[86] Marc Kachelrie?, Theo Fuchs, Stefan Schaller, et al. Advanced single-slice rebinning for tilted spiral cone-beam CT [J]. Medical Physics, 2001, 28(6): 1033-1041.
[87] Michel Defrise, Frédéric Noo, and Hiroyuki Kudo. Rebinning-based algorithms for helical cone-beam CT [J]. Physics in Medicine Biology, 2001, 46: 2911–2937.
[88] Michel Defrise, Frédéric Noo, and Hiroyuki Kudo. Improved 2D rebinning of helical cone-beam CT data using John’s equation [J]. Inverse Problems, 2003, 19: S41-S54.
[89]陈炼,吴志芳,周立业.一种改进的锥束螺旋CT单层重排重建算法[J]. CT理论与应用研究, 2008, 17(1): 7-13.
[90] Hiroyuki Kudo, Frédéric Noo, and Michel Defrise. Performance of quasi-exact cone-beam filtered-backprojection algorithm for axially truncated data [J]. IEEE Transactions on Nuclear Science, 1999, 46: 608–617.
[91] Michel Defrise, Frédéric Noo, and Hiroyuki Kudo. A solution to the long-object problem in helical cone-beam tomography [J]. Physics in Medicine Biology, 2000, 45: 623–643.
[92] Michel Defrise, Frédéric Noo, Hiroyuki Kudo. A combination of rebinning and exact reconstruction algorithms for helical cone-beam CT.
[93] Hiroyuki Kudo, Frédéric Noo, and Michel Defrise. Cone-beam filtered-backprojection algorithm for truncated helical data [J]. Physics in Medicine Biology, 1998, 43: 2885–2909.
[94] Hiroyuki Kudo, Frédéric Noo, and Michel Defrise. Quasi-exact filtered-backprojection algorithm for long-object problem in helical cone-beam tomography [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 902-921.
[95] Hiroyuki Kudo, Frédéric Noo, Michel Defrise, et al. New approximate filtered backprojection algorithm for helical cone-beam CT with redundant data [C]. 2003 IEEE Nuclear Science and Medical Imaging Symposium, 2003, 15: 3211- 3215.
[96] Hiroyuki Kudo, Thomas Rodet, Frédéric Noo, et al. Exact and approximate algorithms for helical cone-beam CT [J]. Physics in Medicine Biology , 2004, 49: 2913–2931
[97] Alexander A. Zamyatin, Katsuyuki Taguchi, and Michael D. Silver. Practical hybrid convolution algorithm for helical CT reconstruction [J]. IEEE Transactions on Nuclear Science, 2006, 53(1): 167-174.
[98] Xiangyang Tang, Jiang Hsieh, Akira Hagiwara, et al. A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT under a circular source trajectory [J]. Physics in Medicine Biology, 2005, 50: 3889–3905.
[99] Xiangyang Tang, Jiang Hsieh, Roy A Nilsen, et al. A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT—helical scanning [J]. Physics in Medicine Biology, 2006, 51: 855–874.
[100] Frank Dennerlein, Holger Kunze, and Frederic Noo. Filtered backprojection reconstruction with depth-dependent filtering [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 82-85.
[101] A. V. Narasimha Dhan, K. P. Anoop, and Kasi Rajgopal. FDK algorithms with no backprojection weight [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 158-161.
[102] Michel Defrise, Frédéric Noo, Hiroyuki Kudo. Quasi-exact region-of-interest reconstruction from helical cone-beam data [C]. IEEE Nuclear Science Symposium, 1999, 1101-1103.
[103] Michel Defris and R. Clack. A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection [J]. IEEE Transactions on Medical Imaging, 1994, 13(1): 186-195.
[104]孙孙孙,王召巴.三维CT在锥角增大时对重建图像质量的影响[J].测试技术学报, 2002, 16(4): 299-301.
[105]王召巴.基于面阵CCD相机的高能X射线工业CT技术研究[D].南京:南京理工大学, 2001.
[106] P. Grangeat. Mathematical framework of cone-beam 3D reconstruction via the first derivative of the Radon transform [J]. Lecture Notes in Mathematics 1497. Mathematical Methods in Tomography. Berlin: Spring-Verlag, 1991, 66~97.
[107] R. Clack, Michel Defris. Cone-beam reconstruction by the use of Radon transform intermediate functions [J]. Journal of Optical Society America 1994, A, 11(2): 580-585.
[108] Y. Weng, G. L. Zeng, and G. T. Gullberg. A reconstruction algorithm for helical cone-beam SPECT [J]. IEEE Transactions on Nuclear Science, 1993, 40(4): 1092-1191.
[109] Ge Wang, Seung Wook Lee. Grangeat-type and Katsevich-type algorithm for Cone-beam CT [J]. CT理论与应用研究, 2003, 12(2): 45-55.
[110] Per-Erik Danielsson. From cone-beam to Radon data in O(N310gN) time [C]. IEEE Nuclear Science Symposium and Medical Imaging Conference, 1993, 1135-1137.
[111] Stefan Schaller, Thomas Flohr, and Peter Steffen. An efficient Fourier method for 3-D Radon inversion in exact cone-beam CT reconstruction [J]. IEEE Transactions on Medical Imaging, 1998, 17(2): 244-250.
[112] S. Schaller, F. Noo, F. Sauer, et al. Exact Radon rebinning algorithm for the long object problem in helical cone-beam CT [J]. IEEE Transactions on Medical Imaging, 2000, 19(5): 361-375.
[113] Hiroyuki Kudo and Tsuneo Saito. Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits [J]. IEEE Transactions on Medical Imaging, 1994, 13(1): 196-211.
[114] Alexander Katsevich. Theoretically exact filtered backprojection type inversion algorithm for spiral CT [J]. SIAM J. APPL. MATH., 2002, 62(6): 2012–2026.
[115] Alexander Katsevich. Analysis of an exact inversion algorithm for spiral cone-beam CT [J]. Physics in Medicine Biology, 2002, 47: 2583–2597.
[116] Alexander Katsevich. An improved exact filtered backprojection algorithm for spiral computed tomography [J]. Advance in Applied Mathematics, 2004, 32: 681–697.
[117] Adam J. Wunderlich. The Katsevich inversion formula for cone-beam computed tomography [D]. Oregon State University, U.S., 2006.
[118] Hengyong Yu and Ge Wang. Studies on implementation of the Katsevich algorithm for spiral cone-beam CT [J]. Journal of X-ray Science and Technology, 2004, 12: 96-116.
[119] Frédéric Noo, Jed Pack, and Dominic Heuscher. Exact helical reconstruction using native cone-beam geometries [J]. Physics in Medicine Biology, 2003, 48: 3787–3818.
[120]马建华陈武凡.不含旋转角度微分的螺旋锥束CT重建[J].中国图象图形学报, 2008, 13 (04): 647-653.
[121]马建华,陈凌剑,颜刚,等.基于混合滤波的避投影数据微分螺旋锥束CT重建[J].南方医科大学学报, 2008, 28(6): 911-914.
[122] Alexander Katsevich, Samit Basu, and Jiang Hsieh. Exact FBP reconstruction for dynamic pitch helical cone beam CT [C]. IEEE Nuclear Science Symposium Conference Record, 2004: 3299-3302.
[123] Yu Zou, Xiaochuan Pan, Dan Xia, et al. Exact image reconstruction in a helical cone-beam scan with a variable pitch [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 4200-4203.
[124] Alexander Katsevich, Samit Basu, and Jiang Hsieh. Exact filtered backprojection reconstruction for dynamic pitch helical cone beam computed tomography [J]. Physics in Medicine Biology, 2004, 49: 3089–3103.
[125] Hengyong Yu, Yangbo Ye, and Ge Wang. Katsevich-type algorithm for variable radius spiral cone-beam CT [C]. Proceeding of SPIE, 2004, 5535: 558-565.
[126] F. Noo, S. Hoppe, F. Dennerlein, et al. A new scheme for view-dependent data differentiation in fan-beam and cone-beam computed tomography [J]. Physics in Medicine Biology, 2007, 52:5393-5414.
[127] Yu Zou and Xiaochuan Pan. Exact image reconstruction on PI-lines from minimum data inhelical cone-beam CT [J]. Physics in Medicine Biology, 2004, 49: 941–959.
[128] Liang Li, Zhiqiang Chen, Yuxiang Xin. General fan-beam and cone-beam reconstruction algorithms formula for freeform trajectories [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 6: 3933-3936.
[129] Liang Li, Zhiqiang Chen, Li Zhang, et al. An exact reconstruction algorithm in variable pitch helical cone-beam CT when PI-line exists [J]. Journal of X-Ray Science and Technology 2006, 14(2): 109-118.
[130] Yu Zou, Xiaochuan Pan, and Dan Xia. PI-line-based image reconstruction in helical cone-beam computed tomography with a variable pitch [J]. Medical Physics, 2005, 3(8): 2639-2648.
[131] Tingliang Zhuang and Guang-Hong Chen. New families of exact fan-beam and cone-beam image reconstruction formulae via filtering the backprojection image of differentiated projection data along singly measured lines [J]. Inverse Problems, 2006, 22: 991–1006.
[132] Lifeng Yu, Dan Xia, Yu Zou, et al. A rebinned backprojection-filtration algorithm for image reconstruction in helical cone-beam CT [J]. Physics in Medicine Biology, 2007, 52: 5497–5508.
[133] Lifeng Yu, Dan Xia, Yu Zou, et al. A Rebinning-type Backprojection-Filtration Algorithm for Image Reconstruction in Helical Cone-beam CT [C]. IEEE Nuclear Science Symposium Conference Record, 2006, 2869-2872.
[134] Dan Xia, Yu Zou, Lifeng Yu, et al. New filtered-backprojection-based algorithms for image reconstruction in fan-beam scans [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 4: 2530-2533.
[135] Yu Zou, Xiaochuan Pan, and Emil Y Sidky. Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan [J]. Physics in Medicine Biology, 2004, 49: 1-15.
[136]谷建伟,张丽,陈志强,等.基于平行PI线段的平行束CT重建[C].清华大学学报(自然科学版), 2007, 47(3): 393-395, 400.
[137] LI Liang, CHEN Zhiqiang, KANG Kejun, et al. Investigation of exact truncated data image reconstruction algorithm on parallel PI-line segments in fan-beam scans [C]. Tsinghua Science and Technology, 2007, 12(3): 337-344.
[138]慧苗,潘晋孝.锥束/多层螺旋CT重建算法在工业CT中的应用及对运算速度的研究[J].中国体视学与图像分析, 2006, 11(3): 163-167.
[139]张全红,路孙年,杨民.锥束工业CT中Feldkamp重建算法的快速实现[J].计算机工程与设计, 2006, 27(6): 931-933.
[140]张晓帆,何明一.基于FDK法的三维CT快速计算方法[J].计算机工程与运用, 2004, 31: 208,209, 221.
[141]张定华,黄魁东,卜昆,等.一种自适应的锥束CT三维图像快速重建方法[P].中国, CN101567090A, 2009.
[142]张顺利,张定华,赵歆波,等.基于最小区域的快速CT图像重建[J].计算机辅助设计与图形学学报, 2009, 21(2): 160-164.
[143] Frédéric Noo, Michel Defrise, RolfClackdoyle, et al. Image reconstruction from fan-beam projections on less than a short scan [J]. Physics in Medicine Biology, 2002, 47: 2525–2546.
[144] Lifeng Yu and Xiaochuan Pan. Preliminary investigation of a new algorithm for image reconstruction in half-scan fan-beam computed tomography [C]. IEEE Nuclear Science Symposium Conference Record, 2002, 2: 979– 983.
[145] Hiroyuki Kudo, Frédéric Noo, Michel Defris, et al. New super-short-scan reconstruction algorithms for fan-beam and cone-beam tomography [C]. IEEE Nuclear Science Symposium record, 2002, 2: 902– 906.
[146] Stacia A. Sawyer, Eric C. Frey, Bin He, et al. Implementation of short-scan reconstruction with compensation for geometric alignment for a micro-CT system [C]. IEEE Nuclear Science Symposium Conference Record, 2003, 4: 2981-2984.
[147] Stefan Hoppe, Frank Dennerlein, Günter Lauritsch, et al. Cone-beam tomography from short-scan circle-plus-arc data measured on a c-arm system [C]. IEEE Nuclear Science Symposium Conference Record, 2006, 1: 2873– 2877.
[148] Kai Zeng, Zhiqiang Chen, Li Zhang, et al. A half-scan error reduction based algorithm [J]. Journal of X-Ray Science and Technology, 2004, 12: 73–82.
[149] Frank Dennerlein, Frédéric Noo, Stefan Hoppe, et al. Evaluation of three analytical methods for reconstruction from cone-beam data on a short circular scan [C]. IEEE Nuclear Science Symposium Conference Record, 2007, 5: 3933-3938.
[150] FU Jian, LU Hongnian. Research of large field of view scan mode for industrial CT [J]. Chinese Journal of Aeronautics, 2003, 16(1): 59-64.
[151]傅健,路孙年.扇束X射线ICT偏置扫描方式及其重构算法[J].光学技术,2003, 29(1): 115-118.
[152]傅健,路孙年.工业CT半扫描成像技术[J].北京航空航天大学学报, 2005, 31(9) :966-969.
[153] Shuai Leng, Tingliang Zhuang, Brian E Nett, et al. Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector [J]. Physics in Medicine Biology, 2005, 50: 1805–1820.
[154] LI Liang, CHEN Zhiqiang, ZHANG Li, et al. A new cone-beam X-ray CT system with a reduced size planar detector [J].高能物理与核物理, 2006, 30(8): 812-817.
[155]李亮,陈志强,张丽,等.一种用于小体积偏置探测器锥束CT系统的反投影滤波重建算法[J]. CT理论与应用研究, 2007, 16(1): 1-9.
[156]傅健,路孙年,龚磊.锥束射线三维大视场工业CT成像方法研究[J].光学技术, 2006, 32(2): 209-212.
[157] Dirk Sch?fer, Michael Grass. Cone-beam filtered backprojection for circular X-ray tomography with off-center detector [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 86-89.
[158] Ge Wang. X-ray micro-CT with a displaced detector array [J]. Medical Physics, 2002, 29 (7): 1634– 1636.
[159] Holger Kunzea and Frank Dennerlein. Cone beam reconstruction with displaced flat panel detector [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 138-141.
[160]傅健,路孙年.一种新颖的ICT扫描方式及其FBP重构算法[J].北京航空航天大学学报, 2003, 29(1): 9-12.
[161]郭艳艳,韩焱,王明泉.大型试件CT重构的一种方法[J].测试技术学报, 2002, 16(4): 305-307.
[162]傅健,路孙年,王孙钧.锥束准三代三维工业CT成像方法研究[J].兵工学报, 2005, 26(6): 776-779.
[163]魏东波,傅健,龚磊,等.大尺寸构件工业CT成像方法[J].北京航空航天大学学报, 2006, 32(12): 1477-1480.
[164] Fu Jian, Lu Hongnian, Li Bing, et al. X-CT imaging method for large objects using double offset scan mode [J]. Nuclear Instruments and Methods in Physics Research A, 2007, 575: 519–523.
[165]赵飞,路孙年,孙翠丽.一种新的二维CT扫描方式及其重建算法[J].光学技术, 2006, 32(2): 284-291.
[166]赵飞,路孙年,孙翠丽. RT二维CT扫描的精确重建[J].光学技术, 2006, 32(4): 518-520.
[167] Ming Chen, Huitao Zhang, Peng Zhang. BPF-based reconstruction algorithm for multiple rotation–translation scan mode [J]. Progress in Natural Science, 2008, 18: 209–216.
[168]陈明.工业CT视野拓展方法及图像伪影校正研究[D].北京:首都师范大学, 2008.
[169]陈明,张慧滔,陈德峰,等.转台单侧多次偏置的旋转扫描模式的重建算法[J].无损检测, 2009, 31(1): 29-34.
[170]祁卫炜.多组锥束扫描数据的CT重建算法[D].北京:首都师范大学, 2008.
[171]陈德峰.大视野锥束CT图像重建的GPU实现方法[D].北京:首都师范大学, 2008.
[172]曾理,邹晓兵,卢艳平.窄角锥束CT的改进扫描方式[J].仪器仪表学报, 2007, 28(7): 1190-1197.
[173] Xiaobing Zou, Li Zeng, Jue Wang, et al. Improved scanning and reconstruction of large objectsby cone-beam industrial computed tomography [C]. Proceeding of the ninth IASTED international conference on signal and image processing, 2007, 146-151.
[174]邹晓兵.锥束工业CT扫描方式与近似重建算法的改进[D].重庆:重庆大学, 2007.
[175]张朝宗,郭志平,张朋,等.工业CT技术和原理[M].北京:科学出版社, 2009.
[176]庞彦伟,王召巴.大型试件的X射线CT检测方法探讨[J].光学技术, 2002, 28(2): 99-102.
[177]王召巴.任意角度入射的三维CT投影方法[J].计量学报, 2002, 23(1): 1-5.
[178]金永,王召巴.扁平构件的三维CT滤波反投影重建算法研究[J].中北大学学报(自然科学版), 2008, 29(2): 180-184.
[179]叶云长.计算机层析成像检测[M].北京:机械工业出版社, 2006.
[180] Chye Hwang Yan, Robert T. Whalen, Gary S. Beaupré, et al. Reconstruction algorithm for polychromatic CT imaging: application to beam hardening correction [J]. IEEE Transactions on Medical Imaging, 2000, 19(1): 1-11.
[181] http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html [OL].
[182]张全红,路孙年,杨民. X-射线工业CT射束硬化校正中噪声的抑制[J].光电工程, 2006, 33(5): 76-80.
[183]孙少华,高文焕,张丽,等.基于多色系统参数的CT硬化校正算法[J].清华大学学报(自然科学版), 2002, 42(12): 1579-1582.
[184] Ming Jiang. Image reconstruction, processing and analysis [M]. http://iria.pku.edu.cn/?jiangm/.
[185] K. C. Tam. Computation of Radon data from cone beam data in cone beam imaging [J]. Journal of Nondestructive Evaluation, 1998, 17(1):1-15.
[186]徐海军,魏东波,傅健,等.三维Radon变换的一种快速解析方法[J]. CT理论与应用研究, 2008, 17(2): 1-7.
[187] Thomas K?hler, Claas Bontus, and Peter Koken. A new approach to handle redundant data in helical cone-beam CT [C]. The 8th International Meeting on Fully Three-dimensional Image Reconstruction in Radiology and Nuclear Medicine. Salt Lake City, Utah, USA, 2005. Utah:University of Utah,2005, 19-22.
[188] Alfred K. Louis, Thomas Weber, and David Theis. Computing reconstruction kernels for circular 3-D cone beam tomography [J]. IEEE Transactions on Medical Imaging, 2008, 27(7): 880-886.
[189] Alexander Katsevich. Improved cone beam local tomography [J]. Inverse Problems, 2006, 22: 627–643.
[190] Yangbo Ye, Hengyong Yu, and Ge Wang. Cone-beam pseudo-lambda tomography [J]. Inverse Problems, 2007, 23: 203–215.
[191] Hengyong Yu, Yuchuan Wei, Yangbo Ye, et al. Lambda tomography with discontinuousscanning trajectories [J]. Physics in Medicine and Biology, 2007, 52:4331–4344.
[192] S. Mallat. A wavelet tour of signal processing [M].北京:机械工业出版社, 2003.
[193]汪璇,曹万强. Hilbert变换及其基本性质分析[J].湖北大学学报(自然科学版), 2008, 30(1): 53-55.
[194]包闻亮,鲍风.信号与通信系统[M] .上海:复旦大学出版社,1993.
[195] Willi A. Kalender. X-ray computed tomography [J]. Physics in Medicine and Biology, 2006, 51: R29–R43.
[196] www.medical.toshiba.com [OL].
[197] Kai Zeng, Zhiqiang Chen. Review of recent developments in cone-beam CT reconstruction algorithms for long-object problems [J]. Image Anal Stereol, 2004, 23: 83-87.
[198] Xiangyang Tang, Jiang Hsieh, Roy A. Nilsen, et al. Helical and axial cone beam filtered backprojection (CB-FBP) reconstruction algorithms using a general window function [C]. IEEE Nuclear Science Symposium Conference Record, 2005, 4: 1863-1866.
[199] L. A. Shepp and B. F. Logan. The Fourier reconstruction of a head section [J]. IEEE Transactions on Nuclear Science, 1974, 21: 21–34.
[200] Ken Chidlow, Torsten M?ller. Rapid emission tomography reconstruction [C]. Proc of the 3rd Eurographics/IEEE TVCG Intenational Workshop on Volume Graphics, Tokyo, Japan, 2003; 45: 15–26.
[201] Yi Sun, Ying Hou, and Jichun Hu. Reduction of artifacts induced by misaligned geometry in cone-beam CT [J]. IEEE Transactions on Biology Engineering, 2007, 54: 1461-1471.
[202] Delia Soimu, Ivan Buliev, Nicolas Pallikarakis. Studies on circular isocentric cone-beam trajectories for 3D image reconstructions using FDK algorithm [J]. Computerized Medical Imaging and Graphics, 2008, 32: 210–220.
[203] Brian E. Nett, Ting-Liang Zhuang, Shuai Leng, et al. Arc based cone-beam reconstruction algorithm using an equal weighting scheme [J]. Journal of X-Ray Science and Technology, 2007, 15: 19–48.
[204] Guorui Yan, Jie Tian, Shouping Zhu, et al. Fast cone-beam CT image reconstruction using GPU hardware [J]. Journal of X-Ray Science and Technology, 2008, 16: 225–234.
[205] Hongzhu Liang, Cishen Zhang, and Ming Yan. A reconstruction algorithm for helical CT imaging on PI-planes [C]. Proceedings of the 28th IEEE EMBS Annual International Conference, New York City, USA, 2006. 2534-2537.
[206] Alexander Katsevich, Katsuyuki Taguchi, and Alexander A. Zamyatin. Formulation of four Katsevich algorithms in native geometry [J]. IEEE Transactions on Medical Imaging, 2006, 25(7): 855-868.
[207] Yu Zou, Xiaochuan Pan. Image reconstruction on PI-lines by use of filtered backprojection in helical cone-beam CT [J]. Physics in Medicine and Biology, 2004, 49: 2717: 2731.
[208] J. Gregor, S. S. Gleason, M. J. Paulus. Cone beam x-ray computed tomography with an offset detector array [C]. IEEE International Conference on Image Processing, Barcelona, 2003: 803-806.
[209] D. Schafer, M. Grass. Cone-beam filtered back-projection for circular X-ray tomography with off-center detector[C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China: 2009: 86-89.
[210] S. Cho, D. Xia, E. Prstdon, et al. Half-fan-based region-of-interest imaging in circular cone-beam CT for radiation therapy[C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China: 2009: 385-388.
[211] Yu Zou, Xiaochuan Pan. An extended data function and its generalized backprojection for image reconstruction in helical cone-beam CT [J]. Physics in Medicine and Biology, 2004, 49: N383-N387.
[212] Lang Li, Zhiqiang Chen, Li Zhang, et al. A backprojection filtered image reconstruction algorithm for circular cone-beam CT [C]. Proceeding of SPIE Medical Imaging, 2006.
[213] Xiaochuan Pan, Emil Y. Sidky, and Michael Vannier. Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction? [J] Inverse Problems, 2009, 25: 1-36.
[214]赵俊,刘尊刚,庄天戈.基于双源双螺旋多层螺旋CT的重建方法[P].中国, CN1751661, 2006.
[215] General Electric Company. Image reconstruction for a CT system implementing a dual fan beam helical scan [P]. USA, 5513236, 1996.
[216] Zeng Li, Mo Shilin, Wang jue, et al. The projection of wavelets and its application in edge detection of computerized tomography [C]. Proceeding of the International Computer Congress 2004 on Wavelet Analysis and its Applications, Singapore. 2004, 1:534-539.
[217] B. De Man, R. Nilsen, E. Drapkin. High performance image reconstruction and implementation [C]. Proceedings Fully 3D Meeting and HPIR Workshop, Lindau, Germany, 2007: 13-16.
[218] B. Heigl, M. Kowarschik. High-speed reconstruction for c-arm computed tomography[C]. Proceedings Fully 3D Meeting and HPIR Workshop, Lindau, Germany, 2007: 25-28.
[219] D. Riabkov, X. Xue, D. Tubbs, et al. Accelerated cone-beam backprojection using GPU-CPU hardware [C]. Proceedings Fully 3D Meeting and HPIR Workshop, Lindau, Germany, 2007: 68-71.
[220] Jiansheng Yang, Xiaohu Guo, Qiang Kong, et al. Parallel implementation of Katsevich’s FBPalgorithm [J]. International Journal of Biomedical Imaging, 2006.
[221] Marc Kachelrie?. High performance exact spiral cone-beam CT image reconstruction [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China, 2009: 9-12.
[222] Wenyuan Bi, Zhiqiang Chen, Li Zhang, et al. Real-time visualize reconstruction procedure using CUDA [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China, 2009: 13-16.
[223] Han Zheng, Yan Kang, Jiren Liu, et al. Implementation of helical cone-beam back-projection filtered reconstruction algorithm on GPU [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China, 2009: 45-48.
[224] Junjun Deng, Hengyong Yu, Jun Ni, et al. A parallel implementation of the Katsevich algorithm for 3-D CT image reconstruction [J]. The Journal of Supercomputing, 2006, 38: 35–47.
[225] Jun Ni, Junjun Deng, Hengyong Yu, et al. Analysis of performance evaluation of parallel Katsevich algorithm for 3-D CT image reconstruction [C]. IEEE First International Multi-Symposiums on Computer and Computational Sciences, 2006, 1: 258-265.
[2] William H. Oldendorf. Isolated flying spot detection of radio density discontinuities-displaying the internal structural pattern of a complex object [P]. IRE Trans. 1961, BME-8, 68-72.
[3] A. M. Cormack. Representation of a function by its line integrals with some radiological applications [J]. Journal of Applied Physics, 1963, 34: 2722-2727.
[4] G T. Herman. Image reconstruction from projections: the fundamentals of computerized tomography [M]. New York: Academic Press, 1980.
[5]庄天戈. CT原理和算法[M].上海:上海交通大学出版社, 1992: 1-99.
[6] Avinash C. Kak, Malcolm Slaney. Principles of computerized tomographic imaging [M]. New York: IEEE Press, 1999.
[7] David Nahamoo, Carl R.Crawford, Avinash C Kak. Design constraints and reconstruction algorithms for traverse-continuous-rotate CT scanners [J]. IEEE Transactions on Biomedical Engineering, 1981, 28(2):79-98.
[8]叶海霞.工业CT窄角扇束卷积反投影并行图像重建研究[D].重庆:重庆大学, 2003.
[9] Crawford, R. Carl, King, F. Kevin. Computed tomography scanning with simultaneous patient translation [J]. Medical Physics, 1990, 17(6): 967-982.
[10] W. A. Kalender, W. Seissler, E. Klotz, et al. Spiral volumetric CT with single-breath-hold technique, continuous transport, and continuous scanner rotation [J]. Radiology, 1990. 176(1): 181-183.
[11] J. S. Arenson, R. Levinson, and D. Freundlich. Dual slice scanner [P]. US Patent No. 5228069, 1993.
[12] Y. Liang, R. A. Kruger. Dual-slice spiral versus single-slice spiral scanning: comparison of the physical performance of two computed tomography scanners [J]. Medical Physics, 1996.23(2): 205-220.
[13] H. Hu. Multi-slice helical CT: Scan and reconstruction [J]. Medical Physics, 1999, 26(1): 5–18.
[14] H. Hu, H. He, W. Foley, et al. Helical CT imaging performance of a new multislice scanner [C]. Proceeding of SPIE Medical Imaging, 3661, San Diego, CA, 1999, 450–461.
[15] K. Taguchi and H. Aradate. Algorithm for image reconstruction in multislice helical CT [J] Medical Physics, 1998, 25(4): 550–561.
[16] Birgit Ertl-Wagner, Lara Eftimov, Jeffrey Blume, et al. Cranial CT with 64-, 16-, 4- andsingle-slice CT systems–comparison of image quality and posterior fossa artifacts in routine brain imaging with standard protocols [J]. European Radiology, 2008, 18(8): 1720-1726.
[17] Patrick J. La Rivière, Xiaochuan Pan. Longitudinal sampling and aliasing in multi-slice helical computed tomography [C]. IEEE Transactions on Medical Imaging, 2001: 79-83.
[18] A. F. Kopp, K. Klingenbeck-Regn, M. Heuschmid, et al. Multislice computed tomography: basic principles and clinical applications [J]. Electromedica, 2000, 68(2): 94-105.
[19] Hui Hu, Tinsu Pan, and Yun Shen. Multislice helical CT: Image temporal resolution [J]. IEEE Transactions on Medical Imaging, 2000, 19(5): 384-390.
[20] L. A. Feldkamp, L. C. Davis, and J. W. Kress. Practical cone-beam algorithm [J]. Journal of Optical Society America, 1984, A 1(6): 612-619.
[21] Bruce D. Smith. Image reconstruction from cone-beam projections: Necessary and sufficient conditions and reconstruction methods [J]. IEEE Transactions on Medical Imaging, 1985, MI-4 (1): 14-25.
[22] Ge Wang, Tein-Hsiang Lin, Ping-chin Cheng, et al. A general cone-beam reconstruction algorithm [J]. IEEE Transactions on Medical Imaging, 1993, 12(3): 486-496.
[23] Ben Wang, Hong Liu, Ge Wang. Generalized Feldkamp image reconstruction from equiangular cone-beam projection data [C]. Proceedings of the 13th IEEE Symposium on Computer-Based Medical Systems, 2000.
[24] H. Kudo, T. Satio. Helical-scan computed tomography using cone-beam projections [C]. Nuclear Science Symposium and Medical Imaging Conference, 1991, 3: 1958– 1962.
[25]毛希平,康克军.三维CT图象精确重建的源点轨迹[J]. CT理论与应用研究, 1997, 6(2): 30-33.
[26] Xiaohui Wang, and Ruola Ning. A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry [J]. IEEE Transactions on Medical Imaging, 1999, 18(9): 815-824.
[27] Xiangyang Tang, and Ruola Ning. A cone beam filtered backprojection (CB-FBP) reconstruction algorithm for a circle-plus-two-arc orbit [J]. Medical Physics, 2001 28(6): 1042-55.
[28] K. C. Tam, G. Lauritsch, K. Sourbelle, et al. Exact (Spiral+Circles) scan region-of-interest cone beam reconstruction via backprojection [J]. IEEE Transaction on Medical Imaging, 2000, 19(5): 376-373.
[29]吕东辉,庄天戈,严壮志,等.体积CT精确重建的完全性条件研究[J].生物医学工程学杂志, 2002, 19(1): 80-83.
[30]牛小明.螺旋锥束工业CT的Katsevich精确重建算法研究[D].重庆:重庆大学, 2008.
[31] D. L. Parker. Optimal short scan convolution reconstruction for fan beam CT [J]. MedicalPhysics, 1982, 9, 254–257.
[32] Lifeng Yu, Xiaochuan Pan. Half-scan fan-beam computed tomography with improved noise and resolution properties [J]. Medical Physics, 2003, 30(10): 2629-2637.
[33] Hiroyuki Kudo, Frédéric Noo, Michel Defrise, et al. New super-short-scan algorithms for fan-beam and cone-beam reconstruction [C]. IEEE Nuclear Science Symposium Conference Record, 2002, 2: 902- 906
[34] Jianhua Ma, Lingjian Chen, Jing Huang, et al. An improved super-short-scan reconstruction for fan-beam computed tomography[C]. 15th IEEE International Conference on Image Processing, 2008, 2936-2939.
[35] Hengyong Yu, Ge Wang. Feldkamp-type VOI reconstruction from super-short-scan cone-beam data [J]. Medical Physics, 2004, 31(6):1357-1362.
[36] Dong Yang and Ruola Ning. FDK half-scan with a heuristic weighting scheme on a flat panel detector-based cone beam CT (FDKHSCW) [J]. International Journal of Biomedical Imaging, 2006: 1–8.
[37] Lei Zhu, and Rebecca Fahrig. Shift-invariant cone-beam FBP reconstruction on not less than a short scan [C]. IFMBE Proceedings,4(14): 2361-2365.
[38] Jicun Hu, Kwok Tam, Jinyi Qi. An approximate short scan helical FDK cone beam algorithm based on curved surfaces satisfying the Tuy's condition [J]. Medical Physics, 2005, 32(6):1529-1536.
[39] Jicun Hu, Kwok Tam, Roger H Johnson, et al. A short scan helical FDK cone beam algorithm based on surfaces satisfying the Tuy’s condition [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 5: 2760–2764.
[40] Frédéric Noo, Hiroyuki Kudo, Michel Defrise. Approximate Short-scan Filtered-backprojection for Helical CB Reconstruction [C]. IEEE Nuclear Science Symposium, 1998. Conference Record, 1998, 3: 2073-2077.
[41] Jed D Pack, Frédéric Noo, and Hiroyuki Kudo. Investigation of saddle trajectories for cardiac CT imaging in cone-beam geometry [J]. Physics in Medicine and Biology, 2004, 49: 2317–2336
[42] Hengyong Yu, Shiying Zhao, Yangbo Ye, et al. Exact BPF and FBP algorithms for nonstandard saddle curves [J]. Medical Physics, 2005, 32(11): 3305-3312.
[43] Dan Xia, Seungryong Cho, Xiaochuan Pan. Reconstructible Volume for Cone-beam CT with a Reduced Saddle Trajectory [C]. IEEE Nuclear Science Symposium Conference Record, 2007, 2630-2632.
[44] Haiquan Yang, Meihua Li, Kazuhito Koizumi, et al. View-independent reconstruction algorithms for cone beam CT with general saddle trajectory [J]. Physics in Medicine and Biology,2006, 51: 3865-3884.
[45] Dan Xia, Seungryong Cho, Xiaochuan Pan. Reconstructible volume for cone-beam CT with a reduced saddle trajectory [C]. Nuclear Science Symposium Conference Record, 2007. IEEE, 4:2630– 2632.
[46] Haiquan Yang, Meihua Li, Kazuhito Koizumi, et al. Exact cone beam reconstruction for a saddle trajectory [J]. Physics in Medicine and Biology, 2006, 51 1157-1172.
[47] Ying Liu, Hong Liu, and Ge Wang. Half-scan cone-beam CT fluoroscopy with multiple x-ray sources [J]. Medical Physics, 2001, 28(7): 166-1471.
[48] Jun Zhao, Ming Jiang, Tiange Zhuang, et al. An exact reconstruction algorithm for triple-source helical cone-beam CT [J]. Journal of X-Ray Science and Technology, 2006, 14: 191–206.
[49] Jun Zhao, Ming Jiang, Tiange Zhuang, et al. Minimum detection window and inter-helix PI-line with triple-source helical cone-beam Scanning [J]. Journal of X-Ray Science and Technology, 2006, 14: 95–107.
[50] Yang Lu, Jun Zhao, and Ge Wang. Exact image reconstruction for triple-source cone-beam CT along saddle trajectories [C]. Proceedings of the SPIE, 2008, 7078: 70780K-70780K-11.
[51] Yang Lu, Jun Zhao. Approximate algorithms for 2N+1 sources cone-beam CT along saddle trajectories [C]. 7th Asian-Pacific Conference on Medical and Biological Engineering, 2008, 19: 229–232.
[52] Jun Zhao, Yannan Jin, Yang Lu, et al. A Filtered Backprojection Algorithm for Triple-Source Helical Cone-Beam CT [J]. IEEE Transactions on Medical Imaging, 2009, 28(3): 384-393.
[53] Yang Lu, Jun Zhao and Ge Wang. Exact image reconstruction with triple-source saddle-curve cone-beam scanning [J]. Physics in Medicine and Biology, 2009, 54: 2971-2991.
[54] S. Valton, F. Peyrin, D. Sappey-Marinie. Generalization of FDK 3D tomographic reconstruction algorithm for an off-centered cone beam geometry [C]. IEEE International Conference on Image Processing, ICIP, 2005, 3: 620-623.
[55] S. Valton, F. Peyrin, D. Sappey-Marinier. A comparative study of three tomographic reconstruction methods in cone beam off-centered circular geometry [C]. 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings, 2006, 228-1231.
[56] S. Valton, F. Peyrin, and D. Sappey-Marinier. A FDK-based reconstruction method for off-centered circular trajectory cone beam tomography [J]. IEEE Transactions on Nuclear Science, 2006, 53(5): 2736-2745.
[57] Satoshi Yoshizawa, Toshiyuki Tanaka, Kazuo Kikuchi. The method of high-accuracy 3D reconstruction for oblique X-ray CT images [C]. SICE Annual Conference, 2007, Kagawa University, Japan, 2007, 146-150.
[58] Jiang Hsieh. Tomographic reconstruction for tilted helical multislice CT [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 864-872.
[59] Ming Yan, Cishen Zhang, Hongzhu Liang, et al. Gantry tilted plane Feldkamp type reconstruction algorithm [C]. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference Shanghai, China, September 1-4, 2005, pp1810-1813.
[60] Frédéric Noo, Michel Defrise, and Hiroyuki Kudo. General reconstruction theory for multislice x-ray computed tomography with a gantry tilt [J]. IEEE Transactions on Medical Imaging, 2004, 23(9): 1109-1116.
[61] Ming Yan, Cishen Zhang, and Hongzhu Liang. An approximate cone beam reconstruction algorithm for gantry-tilted CT using tangential filtering [J]. Development of Computed Tomography Algorithms, 2006.
[62] Shuai Leng, Tingliang Zhuang, Brian E. Nett, et al. Helical cone-beam computed tomography image reconstruction algorithm for a tilted gantry with N-PI data acquisition [J]. Optical Engineering, 2007, 46(1):015004-1—015004-14.
[63]王召巴,陈军.扁平构件的CT重建方法研究[J].应用基础与工程科学学报, 2001, 9(2-3): 222-227.
[64] Yangbo Ye, Shiying Zhao, Hengyong Yu, et al. Exact reconstruction for cone-beam scanning along nonstandard spirals and other curves [C]. Proceeding of SPIE, 2004, 5535: 293-300.
[65] Jiehua Zhu, Shiying Zhao, Hengyong Yu, et al. Numerical studies on Feldkamp-type and Katsevich-type algorithms for cone-beam scanning along nonstandard spirals [C]. Proceeding of SPIE, 2005, 5535: 558-565.
[66] Yangbo Ye, Shiying Zhao, Hengyong Yu, et al. A general exact reconstruction for cone-beam CT via backprojection-filtration [J]. IEEE Transactions on Medical Imaging, 2005, 24(9): 1190-1198.
[67] Hengyong Yu, Yangbo Ye, Shiying Zhao, et al. A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an N-PI Window [J]. Physics in Medicine and Biology, 2005, 50: 2099-2111.
[68] Ge Wang, Yangbo Ye, and Hengyong Yu. Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning [J]. Physics in Medicine and Biology, 2007, 52: R1–R13.
[69]莫仕林,曾理,王珏.基于Master/Slave模式的CT同时代数重建的并行进程[J].工程数学学报, 2004, 21(8): 111-115.
[70] Baodong Liu, Li Zeng, Dongjiang Ji.. Algebraic reconstruction technique class for linear scan CT of long object [C]. Proceedings of the 17th World Conference on Non-destructive Testing,2008.
[71] Baodong Liu; Li Zeng. Parallel SART algorithm of linear scan cone-beam CT for fixed pipeline [J]. Journal of X-Ray Science and Technology, 2009, 17(3): 221-232.
[72] Emil Y Sidky, and Xiaochuan Pan. Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization [J]. Physics in Medicine and Biology, 2008, 53: 4777–4807.
[73] Jiang Hsieh. A nonlinear helical reconstruction algorithm for multislice CT [J]. IEEE Transactions on Nuclear Science, 2002, 49(3): 740-744.
[74] Stefan Schaller, Thomas Flohr, Klaus Klingenbeck, et al. Spiral interpolation algorithm for multislice spiral CT—Part I: Theory [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 822-834.
[75] Theobald Fuchs, Jens Krause, Stefan Schaller, et al. Spiral Interpolation algorithms for multislice spiral CT—Part II: Measurement and evaluation of slice sensitivity profiles and noise at a clinical multislice system [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 835-847.
[76] J. Hsieh, T. Toth, P. Simoni, et al. A multi-slice helical CT reconstruction with generalized weighting [C]. Nuclear Science Symposium Conference Record, 2001 IEEE, 3: 1732-1736.
[77] Wenwu Sun, Siping Chen, Tiange Zhuang. Reconstruction algorithm with improved efficiency and flexibility in multi-slice spiral CT [C]. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, 2005, 1901-1904.
[78]曾凯,陈志强,张丽,等.基于同心圆轨道的锥形束CT重建算法[J].清华大学学报(自然科学版), 2004, 44 (6): 725-727,731.
[79]曾凯,陈志强,张丽,等.圆轨道锥束重建精度与锥角关系的研究[J]. CT理论与应用研究, 2003, 12 (3): 9-16.
[80] Henrik Turbell. Cone-beam reconstruction using filtered backprojection [D]. Link?pings universitet, Link?ping, Sweden, 2001.
[81] M Grass, Th K?hler and R Proksa. 3D cone-beam CT reconstruction for circular trajectories [J]. Physics in Medicine Biology, 2000, 45: 329-347.
[82] Turbell, H. and P.E. Danielsson. Fast Feldkamp reconstruction [C]. International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Egmond aan Zee, The Netherlands, 1999, 311–314.
[83] Frédéric Noo, Michel Defrise, and Rolf Clackdoyle. Single-slice rebinning method for helical cone-beam CT [J]. Physics in Medicine Biology, 1999, 44: 561–570.
[84] H. Bruder, M. Kachelrie?, S. Schaller, et al. Single-slice rebinning reconstruction in spiral cone-beam computed tomography [J]. IEEE Transactions on Medical Imaging, 2000,19(9):873-887.
[85] Marc Kachelrie?, Stefan Schaller, Willi A. Kalender. Advanced single-slice rebinning in cone-beam spiral CT [J]. Medical Physics, 2000, 27(4): 753-772.
[86] Marc Kachelrie?, Theo Fuchs, Stefan Schaller, et al. Advanced single-slice rebinning for tilted spiral cone-beam CT [J]. Medical Physics, 2001, 28(6): 1033-1041.
[87] Michel Defrise, Frédéric Noo, and Hiroyuki Kudo. Rebinning-based algorithms for helical cone-beam CT [J]. Physics in Medicine Biology, 2001, 46: 2911–2937.
[88] Michel Defrise, Frédéric Noo, and Hiroyuki Kudo. Improved 2D rebinning of helical cone-beam CT data using John’s equation [J]. Inverse Problems, 2003, 19: S41-S54.
[89]陈炼,吴志芳,周立业.一种改进的锥束螺旋CT单层重排重建算法[J]. CT理论与应用研究, 2008, 17(1): 7-13.
[90] Hiroyuki Kudo, Frédéric Noo, and Michel Defrise. Performance of quasi-exact cone-beam filtered-backprojection algorithm for axially truncated data [J]. IEEE Transactions on Nuclear Science, 1999, 46: 608–617.
[91] Michel Defrise, Frédéric Noo, and Hiroyuki Kudo. A solution to the long-object problem in helical cone-beam tomography [J]. Physics in Medicine Biology, 2000, 45: 623–643.
[92] Michel Defrise, Frédéric Noo, Hiroyuki Kudo. A combination of rebinning and exact reconstruction algorithms for helical cone-beam CT.
[93] Hiroyuki Kudo, Frédéric Noo, and Michel Defrise. Cone-beam filtered-backprojection algorithm for truncated helical data [J]. Physics in Medicine Biology, 1998, 43: 2885–2909.
[94] Hiroyuki Kudo, Frédéric Noo, and Michel Defrise. Quasi-exact filtered-backprojection algorithm for long-object problem in helical cone-beam tomography [J]. IEEE Transactions on Medical Imaging, 2000, 19(9): 902-921.
[95] Hiroyuki Kudo, Frédéric Noo, Michel Defrise, et al. New approximate filtered backprojection algorithm for helical cone-beam CT with redundant data [C]. 2003 IEEE Nuclear Science and Medical Imaging Symposium, 2003, 15: 3211- 3215.
[96] Hiroyuki Kudo, Thomas Rodet, Frédéric Noo, et al. Exact and approximate algorithms for helical cone-beam CT [J]. Physics in Medicine Biology , 2004, 49: 2913–2931
[97] Alexander A. Zamyatin, Katsuyuki Taguchi, and Michael D. Silver. Practical hybrid convolution algorithm for helical CT reconstruction [J]. IEEE Transactions on Nuclear Science, 2006, 53(1): 167-174.
[98] Xiangyang Tang, Jiang Hsieh, Akira Hagiwara, et al. A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT under a circular source trajectory [J]. Physics in Medicine Biology, 2005, 50: 3889–3905.
[99] Xiangyang Tang, Jiang Hsieh, Roy A Nilsen, et al. A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT—helical scanning [J]. Physics in Medicine Biology, 2006, 51: 855–874.
[100] Frank Dennerlein, Holger Kunze, and Frederic Noo. Filtered backprojection reconstruction with depth-dependent filtering [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 82-85.
[101] A. V. Narasimha Dhan, K. P. Anoop, and Kasi Rajgopal. FDK algorithms with no backprojection weight [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 158-161.
[102] Michel Defrise, Frédéric Noo, Hiroyuki Kudo. Quasi-exact region-of-interest reconstruction from helical cone-beam data [C]. IEEE Nuclear Science Symposium, 1999, 1101-1103.
[103] Michel Defris and R. Clack. A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection [J]. IEEE Transactions on Medical Imaging, 1994, 13(1): 186-195.
[104]孙孙孙,王召巴.三维CT在锥角增大时对重建图像质量的影响[J].测试技术学报, 2002, 16(4): 299-301.
[105]王召巴.基于面阵CCD相机的高能X射线工业CT技术研究[D].南京:南京理工大学, 2001.
[106] P. Grangeat. Mathematical framework of cone-beam 3D reconstruction via the first derivative of the Radon transform [J]. Lecture Notes in Mathematics 1497. Mathematical Methods in Tomography. Berlin: Spring-Verlag, 1991, 66~97.
[107] R. Clack, Michel Defris. Cone-beam reconstruction by the use of Radon transform intermediate functions [J]. Journal of Optical Society America 1994, A, 11(2): 580-585.
[108] Y. Weng, G. L. Zeng, and G. T. Gullberg. A reconstruction algorithm for helical cone-beam SPECT [J]. IEEE Transactions on Nuclear Science, 1993, 40(4): 1092-1191.
[109] Ge Wang, Seung Wook Lee. Grangeat-type and Katsevich-type algorithm for Cone-beam CT [J]. CT理论与应用研究, 2003, 12(2): 45-55.
[110] Per-Erik Danielsson. From cone-beam to Radon data in O(N310gN) time [C]. IEEE Nuclear Science Symposium and Medical Imaging Conference, 1993, 1135-1137.
[111] Stefan Schaller, Thomas Flohr, and Peter Steffen. An efficient Fourier method for 3-D Radon inversion in exact cone-beam CT reconstruction [J]. IEEE Transactions on Medical Imaging, 1998, 17(2): 244-250.
[112] S. Schaller, F. Noo, F. Sauer, et al. Exact Radon rebinning algorithm for the long object problem in helical cone-beam CT [J]. IEEE Transactions on Medical Imaging, 2000, 19(5): 361-375.
[113] Hiroyuki Kudo and Tsuneo Saito. Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits [J]. IEEE Transactions on Medical Imaging, 1994, 13(1): 196-211.
[114] Alexander Katsevich. Theoretically exact filtered backprojection type inversion algorithm for spiral CT [J]. SIAM J. APPL. MATH., 2002, 62(6): 2012–2026.
[115] Alexander Katsevich. Analysis of an exact inversion algorithm for spiral cone-beam CT [J]. Physics in Medicine Biology, 2002, 47: 2583–2597.
[116] Alexander Katsevich. An improved exact filtered backprojection algorithm for spiral computed tomography [J]. Advance in Applied Mathematics, 2004, 32: 681–697.
[117] Adam J. Wunderlich. The Katsevich inversion formula for cone-beam computed tomography [D]. Oregon State University, U.S., 2006.
[118] Hengyong Yu and Ge Wang. Studies on implementation of the Katsevich algorithm for spiral cone-beam CT [J]. Journal of X-ray Science and Technology, 2004, 12: 96-116.
[119] Frédéric Noo, Jed Pack, and Dominic Heuscher. Exact helical reconstruction using native cone-beam geometries [J]. Physics in Medicine Biology, 2003, 48: 3787–3818.
[120]马建华陈武凡.不含旋转角度微分的螺旋锥束CT重建[J].中国图象图形学报, 2008, 13 (04): 647-653.
[121]马建华,陈凌剑,颜刚,等.基于混合滤波的避投影数据微分螺旋锥束CT重建[J].南方医科大学学报, 2008, 28(6): 911-914.
[122] Alexander Katsevich, Samit Basu, and Jiang Hsieh. Exact FBP reconstruction for dynamic pitch helical cone beam CT [C]. IEEE Nuclear Science Symposium Conference Record, 2004: 3299-3302.
[123] Yu Zou, Xiaochuan Pan, Dan Xia, et al. Exact image reconstruction in a helical cone-beam scan with a variable pitch [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 4200-4203.
[124] Alexander Katsevich, Samit Basu, and Jiang Hsieh. Exact filtered backprojection reconstruction for dynamic pitch helical cone beam computed tomography [J]. Physics in Medicine Biology, 2004, 49: 3089–3103.
[125] Hengyong Yu, Yangbo Ye, and Ge Wang. Katsevich-type algorithm for variable radius spiral cone-beam CT [C]. Proceeding of SPIE, 2004, 5535: 558-565.
[126] F. Noo, S. Hoppe, F. Dennerlein, et al. A new scheme for view-dependent data differentiation in fan-beam and cone-beam computed tomography [J]. Physics in Medicine Biology, 2007, 52:5393-5414.
[127] Yu Zou and Xiaochuan Pan. Exact image reconstruction on PI-lines from minimum data inhelical cone-beam CT [J]. Physics in Medicine Biology, 2004, 49: 941–959.
[128] Liang Li, Zhiqiang Chen, Yuxiang Xin. General fan-beam and cone-beam reconstruction algorithms formula for freeform trajectories [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 6: 3933-3936.
[129] Liang Li, Zhiqiang Chen, Li Zhang, et al. An exact reconstruction algorithm in variable pitch helical cone-beam CT when PI-line exists [J]. Journal of X-Ray Science and Technology 2006, 14(2): 109-118.
[130] Yu Zou, Xiaochuan Pan, and Dan Xia. PI-line-based image reconstruction in helical cone-beam computed tomography with a variable pitch [J]. Medical Physics, 2005, 3(8): 2639-2648.
[131] Tingliang Zhuang and Guang-Hong Chen. New families of exact fan-beam and cone-beam image reconstruction formulae via filtering the backprojection image of differentiated projection data along singly measured lines [J]. Inverse Problems, 2006, 22: 991–1006.
[132] Lifeng Yu, Dan Xia, Yu Zou, et al. A rebinned backprojection-filtration algorithm for image reconstruction in helical cone-beam CT [J]. Physics in Medicine Biology, 2007, 52: 5497–5508.
[133] Lifeng Yu, Dan Xia, Yu Zou, et al. A Rebinning-type Backprojection-Filtration Algorithm for Image Reconstruction in Helical Cone-beam CT [C]. IEEE Nuclear Science Symposium Conference Record, 2006, 2869-2872.
[134] Dan Xia, Yu Zou, Lifeng Yu, et al. New filtered-backprojection-based algorithms for image reconstruction in fan-beam scans [C]. IEEE Nuclear Science Symposium Conference Record, 2004, 4: 2530-2533.
[135] Yu Zou, Xiaochuan Pan, and Emil Y Sidky. Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan [J]. Physics in Medicine Biology, 2004, 49: 1-15.
[136]谷建伟,张丽,陈志强,等.基于平行PI线段的平行束CT重建[C].清华大学学报(自然科学版), 2007, 47(3): 393-395, 400.
[137] LI Liang, CHEN Zhiqiang, KANG Kejun, et al. Investigation of exact truncated data image reconstruction algorithm on parallel PI-line segments in fan-beam scans [C]. Tsinghua Science and Technology, 2007, 12(3): 337-344.
[138]慧苗,潘晋孝.锥束/多层螺旋CT重建算法在工业CT中的应用及对运算速度的研究[J].中国体视学与图像分析, 2006, 11(3): 163-167.
[139]张全红,路孙年,杨民.锥束工业CT中Feldkamp重建算法的快速实现[J].计算机工程与设计, 2006, 27(6): 931-933.
[140]张晓帆,何明一.基于FDK法的三维CT快速计算方法[J].计算机工程与运用, 2004, 31: 208,209, 221.
[141]张定华,黄魁东,卜昆,等.一种自适应的锥束CT三维图像快速重建方法[P].中国, CN101567090A, 2009.
[142]张顺利,张定华,赵歆波,等.基于最小区域的快速CT图像重建[J].计算机辅助设计与图形学学报, 2009, 21(2): 160-164.
[143] Frédéric Noo, Michel Defrise, RolfClackdoyle, et al. Image reconstruction from fan-beam projections on less than a short scan [J]. Physics in Medicine Biology, 2002, 47: 2525–2546.
[144] Lifeng Yu and Xiaochuan Pan. Preliminary investigation of a new algorithm for image reconstruction in half-scan fan-beam computed tomography [C]. IEEE Nuclear Science Symposium Conference Record, 2002, 2: 979– 983.
[145] Hiroyuki Kudo, Frédéric Noo, Michel Defris, et al. New super-short-scan reconstruction algorithms for fan-beam and cone-beam tomography [C]. IEEE Nuclear Science Symposium record, 2002, 2: 902– 906.
[146] Stacia A. Sawyer, Eric C. Frey, Bin He, et al. Implementation of short-scan reconstruction with compensation for geometric alignment for a micro-CT system [C]. IEEE Nuclear Science Symposium Conference Record, 2003, 4: 2981-2984.
[147] Stefan Hoppe, Frank Dennerlein, Günter Lauritsch, et al. Cone-beam tomography from short-scan circle-plus-arc data measured on a c-arm system [C]. IEEE Nuclear Science Symposium Conference Record, 2006, 1: 2873– 2877.
[148] Kai Zeng, Zhiqiang Chen, Li Zhang, et al. A half-scan error reduction based algorithm [J]. Journal of X-Ray Science and Technology, 2004, 12: 73–82.
[149] Frank Dennerlein, Frédéric Noo, Stefan Hoppe, et al. Evaluation of three analytical methods for reconstruction from cone-beam data on a short circular scan [C]. IEEE Nuclear Science Symposium Conference Record, 2007, 5: 3933-3938.
[150] FU Jian, LU Hongnian. Research of large field of view scan mode for industrial CT [J]. Chinese Journal of Aeronautics, 2003, 16(1): 59-64.
[151]傅健,路孙年.扇束X射线ICT偏置扫描方式及其重构算法[J].光学技术,2003, 29(1): 115-118.
[152]傅健,路孙年.工业CT半扫描成像技术[J].北京航空航天大学学报, 2005, 31(9) :966-969.
[153] Shuai Leng, Tingliang Zhuang, Brian E Nett, et al. Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector [J]. Physics in Medicine Biology, 2005, 50: 1805–1820.
[154] LI Liang, CHEN Zhiqiang, ZHANG Li, et al. A new cone-beam X-ray CT system with a reduced size planar detector [J].高能物理与核物理, 2006, 30(8): 812-817.
[155]李亮,陈志强,张丽,等.一种用于小体积偏置探测器锥束CT系统的反投影滤波重建算法[J]. CT理论与应用研究, 2007, 16(1): 1-9.
[156]傅健,路孙年,龚磊.锥束射线三维大视场工业CT成像方法研究[J].光学技术, 2006, 32(2): 209-212.
[157] Dirk Sch?fer, Michael Grass. Cone-beam filtered backprojection for circular X-ray tomography with off-center detector [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 86-89.
[158] Ge Wang. X-ray micro-CT with a displaced detector array [J]. Medical Physics, 2002, 29 (7): 1634– 1636.
[159] Holger Kunzea and Frank Dennerlein. Cone beam reconstruction with displaced flat panel detector [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, China, 2009, 138-141.
[160]傅健,路孙年.一种新颖的ICT扫描方式及其FBP重构算法[J].北京航空航天大学学报, 2003, 29(1): 9-12.
[161]郭艳艳,韩焱,王明泉.大型试件CT重构的一种方法[J].测试技术学报, 2002, 16(4): 305-307.
[162]傅健,路孙年,王孙钧.锥束准三代三维工业CT成像方法研究[J].兵工学报, 2005, 26(6): 776-779.
[163]魏东波,傅健,龚磊,等.大尺寸构件工业CT成像方法[J].北京航空航天大学学报, 2006, 32(12): 1477-1480.
[164] Fu Jian, Lu Hongnian, Li Bing, et al. X-CT imaging method for large objects using double offset scan mode [J]. Nuclear Instruments and Methods in Physics Research A, 2007, 575: 519–523.
[165]赵飞,路孙年,孙翠丽.一种新的二维CT扫描方式及其重建算法[J].光学技术, 2006, 32(2): 284-291.
[166]赵飞,路孙年,孙翠丽. RT二维CT扫描的精确重建[J].光学技术, 2006, 32(4): 518-520.
[167] Ming Chen, Huitao Zhang, Peng Zhang. BPF-based reconstruction algorithm for multiple rotation–translation scan mode [J]. Progress in Natural Science, 2008, 18: 209–216.
[168]陈明.工业CT视野拓展方法及图像伪影校正研究[D].北京:首都师范大学, 2008.
[169]陈明,张慧滔,陈德峰,等.转台单侧多次偏置的旋转扫描模式的重建算法[J].无损检测, 2009, 31(1): 29-34.
[170]祁卫炜.多组锥束扫描数据的CT重建算法[D].北京:首都师范大学, 2008.
[171]陈德峰.大视野锥束CT图像重建的GPU实现方法[D].北京:首都师范大学, 2008.
[172]曾理,邹晓兵,卢艳平.窄角锥束CT的改进扫描方式[J].仪器仪表学报, 2007, 28(7): 1190-1197.
[173] Xiaobing Zou, Li Zeng, Jue Wang, et al. Improved scanning and reconstruction of large objectsby cone-beam industrial computed tomography [C]. Proceeding of the ninth IASTED international conference on signal and image processing, 2007, 146-151.
[174]邹晓兵.锥束工业CT扫描方式与近似重建算法的改进[D].重庆:重庆大学, 2007.
[175]张朝宗,郭志平,张朋,等.工业CT技术和原理[M].北京:科学出版社, 2009.
[176]庞彦伟,王召巴.大型试件的X射线CT检测方法探讨[J].光学技术, 2002, 28(2): 99-102.
[177]王召巴.任意角度入射的三维CT投影方法[J].计量学报, 2002, 23(1): 1-5.
[178]金永,王召巴.扁平构件的三维CT滤波反投影重建算法研究[J].中北大学学报(自然科学版), 2008, 29(2): 180-184.
[179]叶云长.计算机层析成像检测[M].北京:机械工业出版社, 2006.
[180] Chye Hwang Yan, Robert T. Whalen, Gary S. Beaupré, et al. Reconstruction algorithm for polychromatic CT imaging: application to beam hardening correction [J]. IEEE Transactions on Medical Imaging, 2000, 19(1): 1-11.
[181] http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html [OL].
[182]张全红,路孙年,杨民. X-射线工业CT射束硬化校正中噪声的抑制[J].光电工程, 2006, 33(5): 76-80.
[183]孙少华,高文焕,张丽,等.基于多色系统参数的CT硬化校正算法[J].清华大学学报(自然科学版), 2002, 42(12): 1579-1582.
[184] Ming Jiang. Image reconstruction, processing and analysis [M]. http://iria.pku.edu.cn/?jiangm/.
[185] K. C. Tam. Computation of Radon data from cone beam data in cone beam imaging [J]. Journal of Nondestructive Evaluation, 1998, 17(1):1-15.
[186]徐海军,魏东波,傅健,等.三维Radon变换的一种快速解析方法[J]. CT理论与应用研究, 2008, 17(2): 1-7.
[187] Thomas K?hler, Claas Bontus, and Peter Koken. A new approach to handle redundant data in helical cone-beam CT [C]. The 8th International Meeting on Fully Three-dimensional Image Reconstruction in Radiology and Nuclear Medicine. Salt Lake City, Utah, USA, 2005. Utah:University of Utah,2005, 19-22.
[188] Alfred K. Louis, Thomas Weber, and David Theis. Computing reconstruction kernels for circular 3-D cone beam tomography [J]. IEEE Transactions on Medical Imaging, 2008, 27(7): 880-886.
[189] Alexander Katsevich. Improved cone beam local tomography [J]. Inverse Problems, 2006, 22: 627–643.
[190] Yangbo Ye, Hengyong Yu, and Ge Wang. Cone-beam pseudo-lambda tomography [J]. Inverse Problems, 2007, 23: 203–215.
[191] Hengyong Yu, Yuchuan Wei, Yangbo Ye, et al. Lambda tomography with discontinuousscanning trajectories [J]. Physics in Medicine and Biology, 2007, 52:4331–4344.
[192] S. Mallat. A wavelet tour of signal processing [M].北京:机械工业出版社, 2003.
[193]汪璇,曹万强. Hilbert变换及其基本性质分析[J].湖北大学学报(自然科学版), 2008, 30(1): 53-55.
[194]包闻亮,鲍风.信号与通信系统[M] .上海:复旦大学出版社,1993.
[195] Willi A. Kalender. X-ray computed tomography [J]. Physics in Medicine and Biology, 2006, 51: R29–R43.
[196] www.medical.toshiba.com [OL].
[197] Kai Zeng, Zhiqiang Chen. Review of recent developments in cone-beam CT reconstruction algorithms for long-object problems [J]. Image Anal Stereol, 2004, 23: 83-87.
[198] Xiangyang Tang, Jiang Hsieh, Roy A. Nilsen, et al. Helical and axial cone beam filtered backprojection (CB-FBP) reconstruction algorithms using a general window function [C]. IEEE Nuclear Science Symposium Conference Record, 2005, 4: 1863-1866.
[199] L. A. Shepp and B. F. Logan. The Fourier reconstruction of a head section [J]. IEEE Transactions on Nuclear Science, 1974, 21: 21–34.
[200] Ken Chidlow, Torsten M?ller. Rapid emission tomography reconstruction [C]. Proc of the 3rd Eurographics/IEEE TVCG Intenational Workshop on Volume Graphics, Tokyo, Japan, 2003; 45: 15–26.
[201] Yi Sun, Ying Hou, and Jichun Hu. Reduction of artifacts induced by misaligned geometry in cone-beam CT [J]. IEEE Transactions on Biology Engineering, 2007, 54: 1461-1471.
[202] Delia Soimu, Ivan Buliev, Nicolas Pallikarakis. Studies on circular isocentric cone-beam trajectories for 3D image reconstructions using FDK algorithm [J]. Computerized Medical Imaging and Graphics, 2008, 32: 210–220.
[203] Brian E. Nett, Ting-Liang Zhuang, Shuai Leng, et al. Arc based cone-beam reconstruction algorithm using an equal weighting scheme [J]. Journal of X-Ray Science and Technology, 2007, 15: 19–48.
[204] Guorui Yan, Jie Tian, Shouping Zhu, et al. Fast cone-beam CT image reconstruction using GPU hardware [J]. Journal of X-Ray Science and Technology, 2008, 16: 225–234.
[205] Hongzhu Liang, Cishen Zhang, and Ming Yan. A reconstruction algorithm for helical CT imaging on PI-planes [C]. Proceedings of the 28th IEEE EMBS Annual International Conference, New York City, USA, 2006. 2534-2537.
[206] Alexander Katsevich, Katsuyuki Taguchi, and Alexander A. Zamyatin. Formulation of four Katsevich algorithms in native geometry [J]. IEEE Transactions on Medical Imaging, 2006, 25(7): 855-868.
[207] Yu Zou, Xiaochuan Pan. Image reconstruction on PI-lines by use of filtered backprojection in helical cone-beam CT [J]. Physics in Medicine and Biology, 2004, 49: 2717: 2731.
[208] J. Gregor, S. S. Gleason, M. J. Paulus. Cone beam x-ray computed tomography with an offset detector array [C]. IEEE International Conference on Image Processing, Barcelona, 2003: 803-806.
[209] D. Schafer, M. Grass. Cone-beam filtered back-projection for circular X-ray tomography with off-center detector[C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China: 2009: 86-89.
[210] S. Cho, D. Xia, E. Prstdon, et al. Half-fan-based region-of-interest imaging in circular cone-beam CT for radiation therapy[C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China: 2009: 385-388.
[211] Yu Zou, Xiaochuan Pan. An extended data function and its generalized backprojection for image reconstruction in helical cone-beam CT [J]. Physics in Medicine and Biology, 2004, 49: N383-N387.
[212] Lang Li, Zhiqiang Chen, Li Zhang, et al. A backprojection filtered image reconstruction algorithm for circular cone-beam CT [C]. Proceeding of SPIE Medical Imaging, 2006.
[213] Xiaochuan Pan, Emil Y. Sidky, and Michael Vannier. Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction? [J] Inverse Problems, 2009, 25: 1-36.
[214]赵俊,刘尊刚,庄天戈.基于双源双螺旋多层螺旋CT的重建方法[P].中国, CN1751661, 2006.
[215] General Electric Company. Image reconstruction for a CT system implementing a dual fan beam helical scan [P]. USA, 5513236, 1996.
[216] Zeng Li, Mo Shilin, Wang jue, et al. The projection of wavelets and its application in edge detection of computerized tomography [C]. Proceeding of the International Computer Congress 2004 on Wavelet Analysis and its Applications, Singapore. 2004, 1:534-539.
[217] B. De Man, R. Nilsen, E. Drapkin. High performance image reconstruction and implementation [C]. Proceedings Fully 3D Meeting and HPIR Workshop, Lindau, Germany, 2007: 13-16.
[218] B. Heigl, M. Kowarschik. High-speed reconstruction for c-arm computed tomography[C]. Proceedings Fully 3D Meeting and HPIR Workshop, Lindau, Germany, 2007: 25-28.
[219] D. Riabkov, X. Xue, D. Tubbs, et al. Accelerated cone-beam backprojection using GPU-CPU hardware [C]. Proceedings Fully 3D Meeting and HPIR Workshop, Lindau, Germany, 2007: 68-71.
[220] Jiansheng Yang, Xiaohu Guo, Qiang Kong, et al. Parallel implementation of Katsevich’s FBPalgorithm [J]. International Journal of Biomedical Imaging, 2006.
[221] Marc Kachelrie?. High performance exact spiral cone-beam CT image reconstruction [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China, 2009: 9-12.
[222] Wenyuan Bi, Zhiqiang Chen, Li Zhang, et al. Real-time visualize reconstruction procedure using CUDA [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China, 2009: 13-16.
[223] Han Zheng, Yan Kang, Jiren Liu, et al. Implementation of helical cone-beam back-projection filtered reconstruction algorithm on GPU [C]. Proceeding of 10th Fully 3D Meeting and 2nd HPIR workshop, Beijing, P.R. China, 2009: 45-48.
[224] Junjun Deng, Hengyong Yu, Jun Ni, et al. A parallel implementation of the Katsevich algorithm for 3-D CT image reconstruction [J]. The Journal of Supercomputing, 2006, 38: 35–47.
[225] Jun Ni, Junjun Deng, Hengyong Yu, et al. Analysis of performance evaluation of parallel Katsevich algorithm for 3-D CT image reconstruction [C]. IEEE First International Multi-Symposiums on Computer and Computational Sciences, 2006, 1: 258-265.