CT系统中射束硬化校正算法研究
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摘要
射束硬化是由X射线束能谱的多能性和衰减系数与能量的相关性造成的。多能X射线穿过物体时,能量较低的X光子由于光电效应优先被吸收,使得穿透物质的X射线高能成分比例增加,表现为平均能量升高,从而使射线随贯穿长度增加,变得更易穿透,频谱分布的峰值向较高的能量方向移动,这就是射束硬化效应。它会导致密度均匀的被测物体切片在重建CT图像上表现为亮度不一,图像上的像素值分布呈中间黑边缘亮的“茶杯”状,即“杯状”伪影。
目前,国内外对射束硬化校正的研究已取得很大进展,达到一定的硬化校正效果,但还不够完善,仍需进一步研究。
本文对传统线性化校正方法做了两点改进:(1)对传统多项式拟合校正方法在等效衰减系数的求法上做了改进:改进方法对靠近原点的几组数据进行直线拟合,选取该拟合直线的斜率代替传统方法中的拟合曲线在零点处的导数值,以拟合直线的斜率作为单色时的等效衰减系数,更接近实际,有效地减小了误差。(2)对拟合函数做了进一步的改进:以更能满足射束硬化曲线拟合相关要求的指数函数代替传统方法中的多项式函数,实验结果表明校正效果更好。
本文还研究了基于统计迭代的硬化校正方法,根据能谱的连续性和探测到的光子数服从Poisson分布这一规律建立数学模型,并在传统迭代重建算法的基础上,借用统计的方法进行参数估计,实验结果表明该方法有效提高了重建图像质量。
Beam-hardening is caused by polychromatic energy spectrum and energy dependency attenuation coefficient. When the polychromatic rays cut through the object, the lower energy X-photon absorption as the photoelectric effect was first made through X-ray high-energy component material proportion of the increase reflected higher average energy, so with the transmitted ray thickness becomes more penetrating, the spectrum distribution of the peak moves to higher energy, which is beam hardening effect. It will lead to a uniform density in the reconstruction of the measured object slice CT images showed different brightness, the image pixel value distribution is the brightest among the black edges "cup" shape, that is, "cup" artifacts.
The present research on beam hardening correction of great progress has been made to achieve a certain effect of beam hardening correction, but still not perfect, still needs further study.
This paper has two improvements on traditional method of linearization correction: First, the traditional method of the equivalent polynomial correction method for finding the attenuation coefficient has been improved, The method of close to the origin of several groups of data lines fitting, fitting the slope selected to replace the traditional methods of fitting curves in the zeros of derivatives, in order to fit the slope as the equivalent attenuation coefficient of monochromatic, effectively reduced error. Second,the fitting function has been further improved, To better meet the relevant requirements of beam hardening curve, exponential function instead of the traditional method of polynomial functions, experimental results show that the correction results is better with exponential function.
This paper also studied the hardening correction based on statistical iterative method. And build the math model according to the continuity of energy spectrum and the number of photons detected obeys Poisson distribution. Then make parameter estimation with the statistical method on the basis of traditional reconstruction algorithm. Experimental results show that the method effectively improves the image quality.
目前,国内外对射束硬化校正的研究已取得很大进展,达到一定的硬化校正效果,但还不够完善,仍需进一步研究。
本文对传统线性化校正方法做了两点改进:(1)对传统多项式拟合校正方法在等效衰减系数的求法上做了改进:改进方法对靠近原点的几组数据进行直线拟合,选取该拟合直线的斜率代替传统方法中的拟合曲线在零点处的导数值,以拟合直线的斜率作为单色时的等效衰减系数,更接近实际,有效地减小了误差。(2)对拟合函数做了进一步的改进:以更能满足射束硬化曲线拟合相关要求的指数函数代替传统方法中的多项式函数,实验结果表明校正效果更好。
本文还研究了基于统计迭代的硬化校正方法,根据能谱的连续性和探测到的光子数服从Poisson分布这一规律建立数学模型,并在传统迭代重建算法的基础上,借用统计的方法进行参数估计,实验结果表明该方法有效提高了重建图像质量。
Beam-hardening is caused by polychromatic energy spectrum and energy dependency attenuation coefficient. When the polychromatic rays cut through the object, the lower energy X-photon absorption as the photoelectric effect was first made through X-ray high-energy component material proportion of the increase reflected higher average energy, so with the transmitted ray thickness becomes more penetrating, the spectrum distribution of the peak moves to higher energy, which is beam hardening effect. It will lead to a uniform density in the reconstruction of the measured object slice CT images showed different brightness, the image pixel value distribution is the brightest among the black edges "cup" shape, that is, "cup" artifacts.
The present research on beam hardening correction of great progress has been made to achieve a certain effect of beam hardening correction, but still not perfect, still needs further study.
This paper has two improvements on traditional method of linearization correction: First, the traditional method of the equivalent polynomial correction method for finding the attenuation coefficient has been improved, The method of close to the origin of several groups of data lines fitting, fitting the slope selected to replace the traditional methods of fitting curves in the zeros of derivatives, in order to fit the slope as the equivalent attenuation coefficient of monochromatic, effectively reduced error. Second,the fitting function has been further improved, To better meet the relevant requirements of beam hardening curve, exponential function instead of the traditional method of polynomial functions, experimental results show that the correction results is better with exponential function.
This paper also studied the hardening correction based on statistical iterative method. And build the math model according to the continuity of energy spectrum and the number of photons detected obeys Poisson distribution. Then make parameter estimation with the statistical method on the basis of traditional reconstruction algorithm. Experimental results show that the method effectively improves the image quality.
引文
[1]邹晶. X射线能量谱恢复及射束硬化、散射研究[J]. CT理论与应用研究, 2006.
[2]庄天戈. CT原理与算法[M].上海.上海交通大学出版社, 1992.
[3] Yan C H,Robert T W,Gary S B,et a1.Reconstruction algorithm for polychromatic CT imaging:application to beam hardening correction[J].IEEE Transactions on Medical Imaging,2000,19(1):1-11.
[4]陈立成.层析成象的数学方法与应用[D].西南交通大学, 1991.
[5] [美]Jiang Hsieh.计算机断层成像技术—原理、设计、伪像和进展[M].科学出版社.2005.
[6]彭光含,杨学选. X-ICT中连续谱服从Gauss分布的硬化修正研究[J].无损检测.2006.
[7]彭光含.连续谱X射线在ICT中的能谱硬化与散射修正[J].重庆大学.2006.
[8] R, J, Jennings. A method for comparing beam hardening filter materials for diagnostic radiology[J]. Medical Physics,1998,15 (4):588-599.
[9] HAMMERSBERG P, MANGARD M. Correction for beam hardening artefacts in computerized tomography [J].J.X-ray Sci. Technol , 1998, 8:75-93.
[10]谷建伟,张丽.圆轨迹锥束CT的伪影成因和校正方法综述[C].北京:CT和三维成像学术年会论文集,2004:12-16.
[11] Herman G T .Correction for beam hardening in computed tomography[J].Phys Med Biol,1979,24(1):81—106.
[12] Herman G T. Imange Reconstruction from Projections: The Fundamentals of Computerized Tomography [M].New York: Academic Press, 1980.
[13]杨民,路宏年,路远.CT重构中射线硬化校正研究[J].光学技术,2003,29(2):177-182.
[14] J. Hsieh. Computed Tomography -Principles,Designs,Artifacts and Recent Advances. SPIE Press ,Bellingham,WA,2003.
[15] O.Nalcioglu, R.Y.Lou. Post-reconstruction method for beam hardening in computedtomography [J]. Phys. Med. Biol , 1979, 24:330-340.
[16] Jiang Hsieh. Computed Tomography Principles, Design, Artifacts, and Recent Advances [M ]. Bellingham, WA: SPIE Optical Engineering Press, 2004:128-131.
[17] S Basu, Y Bresler . An O (N21ogN) filtered back projection reconstruction algorithm for tomography [J].IEEE Trans. Image Processing,2000,9 (10):1760- 1773.
[18]杨福家.原子物理学[M].高等教育出版社,2000
[19]李承华.辐射技术基础[M].原子能出版社,1988
[20] GEANT4 Web Site:http://geant4.web.cern.ch.
[21] Rodenas , J.Gallardo , S.Burgos , M.C. Simulation Models to Obtain X-ray Spectra Using the Compton Scattering Technique [A]. Physics and Control,2003. Proeeedings.2003 International Conference[C], 2003, 8(1):228-231.
[22]谢忠信,赵宗玲,张玉斌,陈远盘. X射线光谱分析.北京:科学出版社,1982
[23]王建光.X射线能量谱分布的研究[D].北京:首都师范大学硕士论文,2005.6.
[24] Hsieh J. Computed tomography-principles, artifacts, and recent advances[M]. Bellingham: SPIE Press, 2003.
[25] BARRETT H H,SWINDEL W著,庄天戈等译.放射成像-图像形成、检测和处理的理论[M].北京:科学出版社,1988:52-55.
[26]孙少华,高文焕等.基于多色系统参数的硬化校正算法[J].清华大学学报,Vol.42,No.12,2002
[27] E Van Casteele , D Van Dyck , Jsijbers and E Raman. An Energy-based Beam Hardening Model in Tomography [J]. Phys.Med.Biol.47, 2002
[28] Chye Hwang Yan, Robert T. Whalen. Reconstruction Algorithm for Polychromatic CT imaging: Application to Beam Hardening Correction [J].IEEE Trans. Med. Imag, 2002, 19(1).
[29] A J Coleman and M Sinclair. A Beam Hardening Correcting Using Dual-energy Computed Tomography [J]. Phys. Med. Biol., Vol. 30, No.11, 1985
[30] GOODSITT M M . Beam hardening errors in post-processing dual energy quantitative computed tomography [J」.Med.Phys,1995,22(7):1039-1047.
[31]王凯,张定华,刘晶,等.采用3D Gaussian facet模型的亚体素表面检测[J].计算机辅助设计与图形学学报,2007,19(9):1100-1106.
[32]李庆扬.数值分析基础教程[M].北京:高等教育出版社,2001.
[33]施妙根,顾丽珍.科学和工程计算基础[M].北京:清华大学出版社,1999.
[34] Weijer J V D, Boomgaard R V D. Least squares and robust estimation of local image structure [J].International Journal of Computer Vision,2005,64(23):143-155.
[35]张全红,路宏年,杨民.基于重投影的多项式拟合校正射束硬化[J].光学技术,2005,31(4): 633-635.
[36]黄魁东,张定华,孔永茂,等.基于切片轮廓重投影的锥束CT射束硬化校正方法[J].仪器仪表学报,2008,29(9):1893-1877.
[37]吉昂,陶光仪,卓尚军,罗立强.X射线荧光光谱分析[M].北京:科学出版社,2005.
[38]余晓锷.优化CT图像金属伪影消除算法研究[D].广州:南方医科大学博士论文.2009.4
[39] G.T.赫尔曼著,严洪范等译.由投影重建图像[M].北京:科学出版社,1985.
[40] Alvarez.E, Macovski A. Energy-selective reconstruction in x-ray computed Tomography[J],Phys.Med.Biol,1976, 21(5):733-744.
[41] Marshall W H, Alvarez R E, A. Macovski. Initial results with prereconstruction dual-energy Computed Tomography[J].Radiology,1981,140:421-430.
[42]魏宗舒.概率论与数理统计教程[M].北京:高等教育出版社,1985.
[2]庄天戈. CT原理与算法[M].上海.上海交通大学出版社, 1992.
[3] Yan C H,Robert T W,Gary S B,et a1.Reconstruction algorithm for polychromatic CT imaging:application to beam hardening correction[J].IEEE Transactions on Medical Imaging,2000,19(1):1-11.
[4]陈立成.层析成象的数学方法与应用[D].西南交通大学, 1991.
[5] [美]Jiang Hsieh.计算机断层成像技术—原理、设计、伪像和进展[M].科学出版社.2005.
[6]彭光含,杨学选. X-ICT中连续谱服从Gauss分布的硬化修正研究[J].无损检测.2006.
[7]彭光含.连续谱X射线在ICT中的能谱硬化与散射修正[J].重庆大学.2006.
[8] R, J, Jennings. A method for comparing beam hardening filter materials for diagnostic radiology[J]. Medical Physics,1998,15 (4):588-599.
[9] HAMMERSBERG P, MANGARD M. Correction for beam hardening artefacts in computerized tomography [J].J.X-ray Sci. Technol , 1998, 8:75-93.
[10]谷建伟,张丽.圆轨迹锥束CT的伪影成因和校正方法综述[C].北京:CT和三维成像学术年会论文集,2004:12-16.
[11] Herman G T .Correction for beam hardening in computed tomography[J].Phys Med Biol,1979,24(1):81—106.
[12] Herman G T. Imange Reconstruction from Projections: The Fundamentals of Computerized Tomography [M].New York: Academic Press, 1980.
[13]杨民,路宏年,路远.CT重构中射线硬化校正研究[J].光学技术,2003,29(2):177-182.
[14] J. Hsieh. Computed Tomography -Principles,Designs,Artifacts and Recent Advances. SPIE Press ,Bellingham,WA,2003.
[15] O.Nalcioglu, R.Y.Lou. Post-reconstruction method for beam hardening in computedtomography [J]. Phys. Med. Biol , 1979, 24:330-340.
[16] Jiang Hsieh. Computed Tomography Principles, Design, Artifacts, and Recent Advances [M ]. Bellingham, WA: SPIE Optical Engineering Press, 2004:128-131.
[17] S Basu, Y Bresler . An O (N21ogN) filtered back projection reconstruction algorithm for tomography [J].IEEE Trans. Image Processing,2000,9 (10):1760- 1773.
[18]杨福家.原子物理学[M].高等教育出版社,2000
[19]李承华.辐射技术基础[M].原子能出版社,1988
[20] GEANT4 Web Site:http://geant4.web.cern.ch.
[21] Rodenas , J.Gallardo , S.Burgos , M.C. Simulation Models to Obtain X-ray Spectra Using the Compton Scattering Technique [A]. Physics and Control,2003. Proeeedings.2003 International Conference[C], 2003, 8(1):228-231.
[22]谢忠信,赵宗玲,张玉斌,陈远盘. X射线光谱分析.北京:科学出版社,1982
[23]王建光.X射线能量谱分布的研究[D].北京:首都师范大学硕士论文,2005.6.
[24] Hsieh J. Computed tomography-principles, artifacts, and recent advances[M]. Bellingham: SPIE Press, 2003.
[25] BARRETT H H,SWINDEL W著,庄天戈等译.放射成像-图像形成、检测和处理的理论[M].北京:科学出版社,1988:52-55.
[26]孙少华,高文焕等.基于多色系统参数的硬化校正算法[J].清华大学学报,Vol.42,No.12,2002
[27] E Van Casteele , D Van Dyck , Jsijbers and E Raman. An Energy-based Beam Hardening Model in Tomography [J]. Phys.Med.Biol.47, 2002
[28] Chye Hwang Yan, Robert T. Whalen. Reconstruction Algorithm for Polychromatic CT imaging: Application to Beam Hardening Correction [J].IEEE Trans. Med. Imag, 2002, 19(1).
[29] A J Coleman and M Sinclair. A Beam Hardening Correcting Using Dual-energy Computed Tomography [J]. Phys. Med. Biol., Vol. 30, No.11, 1985
[30] GOODSITT M M . Beam hardening errors in post-processing dual energy quantitative computed tomography [J」.Med.Phys,1995,22(7):1039-1047.
[31]王凯,张定华,刘晶,等.采用3D Gaussian facet模型的亚体素表面检测[J].计算机辅助设计与图形学学报,2007,19(9):1100-1106.
[32]李庆扬.数值分析基础教程[M].北京:高等教育出版社,2001.
[33]施妙根,顾丽珍.科学和工程计算基础[M].北京:清华大学出版社,1999.
[34] Weijer J V D, Boomgaard R V D. Least squares and robust estimation of local image structure [J].International Journal of Computer Vision,2005,64(23):143-155.
[35]张全红,路宏年,杨民.基于重投影的多项式拟合校正射束硬化[J].光学技术,2005,31(4): 633-635.
[36]黄魁东,张定华,孔永茂,等.基于切片轮廓重投影的锥束CT射束硬化校正方法[J].仪器仪表学报,2008,29(9):1893-1877.
[37]吉昂,陶光仪,卓尚军,罗立强.X射线荧光光谱分析[M].北京:科学出版社,2005.
[38]余晓锷.优化CT图像金属伪影消除算法研究[D].广州:南方医科大学博士论文.2009.4
[39] G.T.赫尔曼著,严洪范等译.由投影重建图像[M].北京:科学出版社,1985.
[40] Alvarez.E, Macovski A. Energy-selective reconstruction in x-ray computed Tomography[J],Phys.Med.Biol,1976, 21(5):733-744.
[41] Marshall W H, Alvarez R E, A. Macovski. Initial results with prereconstruction dual-energy Computed Tomography[J].Radiology,1981,140:421-430.
[42]魏宗舒.概率论与数理统计教程[M].北京:高等教育出版社,1985.