CT系统参数标定及成像
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摘要
根据Beer-lambert定律建立X射线衰减的微分方程模型,基于最小二乘思想建立目标规划模型,确定给定CT系统的标定参数;建立CT图像重建的迭代模型,并利用Richardson算法求解未知介质的各项参数;采用R-L滤波函数建立图像重建降噪模型,重构受噪声影响的未知介质图像;对问题一中标定的参数进行精度和稳定性分析并设计新的模板。
A differential equation system for X-ray attenuation model is built according to Beer-lambert's law, and the parameters for the given templet of the CT system are calibrated based on least square thought.An iterative model for reconstruction of CT image is built and the parameters for the unknown media with Richardson method are figured out. Then, the denoising model is reconstructed with the image obtained from R-L filter function and the image of the unknown media affected by the noise is reconstructed as well.Finally, the accuracy and the stability of the parameters are analyzed and a new templet for the CT system is designed.
A differential equation system for X-ray attenuation model is built according to Beer-lambert's law, and the parameters for the given templet of the CT system are calibrated based on least square thought.An iterative model for reconstruction of CT image is built and the parameters for the unknown media with Richardson method are figured out. Then, the denoising model is reconstructed with the image obtained from R-L filter function and the image of the unknown media affected by the noise is reconstructed as well.Finally, the accuracy and the stability of the parameters are analyzed and a new templet for the CT system is designed.
引文
[1]全国大学生数学建模竞赛组委会.2017高教社杯全国大学生数学建模竞赛(CUMCM)题目A题[EB/OL].(2017-09-13)[2017-09-14].http://www.mcm.edu.cn/.
[2]姜启源,谢金星,叶俊.数学模型[M].4版.北京:高等教育出版社,2011.
[3]涂修佳.基于正弦图的扇束CT系统投影旋转中心自动标定方法[C]//中国体视学学会CT理论与应用分会.全国射线数字成像与CT新技术研讨会论文集.绵阳:[出版者不详],2012:37-42.
[4]宗殿瑞,宋文臣,刘朋振.最小二乘法应用探讨[J].青岛化工学院学报,1998(3):296-302.
[5]李琼.迭代重建技术在低剂量胸部CT中应用的体模及临床研究[D].上海:第二军医大学,2013.
[6]Bessenrodt C,Tewari V,Willigenburg S V.Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions[J].Journal of Combinatorial Theory,Series A,2016,137:179-206.
[7]闫河,闫卫军,李唯唯.基于Lucy-Richardson算法的图像复原[J].计算机工程,2010,36(15):204-205,210.
[8]陈颍滨,邓彬,王宏强.基于投影-切片定理的转台成像算法[J].信号处理,2011(9):1380-1384.
[9]王丽萍,吴秋花,邱飞岳,等.局部搜索与改进MOPSO的混合优化算法及其应用[J].计算机科学,2012(11):174-178,200.
[2]姜启源,谢金星,叶俊.数学模型[M].4版.北京:高等教育出版社,2011.
[3]涂修佳.基于正弦图的扇束CT系统投影旋转中心自动标定方法[C]//中国体视学学会CT理论与应用分会.全国射线数字成像与CT新技术研讨会论文集.绵阳:[出版者不详],2012:37-42.
[4]宗殿瑞,宋文臣,刘朋振.最小二乘法应用探讨[J].青岛化工学院学报,1998(3):296-302.
[5]李琼.迭代重建技术在低剂量胸部CT中应用的体模及临床研究[D].上海:第二军医大学,2013.
[6]Bessenrodt C,Tewari V,Willigenburg S V.Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions[J].Journal of Combinatorial Theory,Series A,2016,137:179-206.
[7]闫河,闫卫军,李唯唯.基于Lucy-Richardson算法的图像复原[J].计算机工程,2010,36(15):204-205,210.
[8]陈颍滨,邓彬,王宏强.基于投影-切片定理的转台成像算法[J].信号处理,2011(9):1380-1384.
[9]王丽萍,吴秋花,邱飞岳,等.局部搜索与改进MOPSO的混合优化算法及其应用[J].计算机科学,2012(11):174-178,200.