北京航空航天大学学报 ›› 2005, Vol. 31 ›› Issue (10): 1135-1139.

• 论文 • 上一篇    下一篇

三维CT重建几何参数的非线性最小二乘估计

杨民, 路宏年, 孔凡琴, 张全红   

  1. 北京航空航天大学 机械工程及自动化学院, 北京 100083
  • 收稿日期:2004-07-05 出版日期:2005-10-31 发布日期:2010-09-20
  • 作者简介:杨 民(1975-),男,陕西蒲城人,博士后, minyang.ndt@.263.net.
  • 基金资助:

    国家自然科学基金资助项目(60402042)

Non-linear least square estimation of geometrical parameters for cone-beam three dimensional computed tomography

Yang Min, Lu Hongnian, Kong Fanqin, Zhang Quanhong   

  1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2004-07-05 Online:2005-10-31 Published:2010-09-20

摘要: 重建几何参数的精度是3D-CT(Three Dimensional Computed Tomography)重建中严格控制的指标,在实际的X射线扫描成像中,这些参数无法直接测量得到,从而难以保证其精度.介绍了利用非线性最小二乘估计Feldkamp三维重建几何参数的方法,根据空间质点质心的投影位置与其投影的质心位置重合的原理,通过计算空间质点(实验中采用近似质点的目标体)投影质心坐标,求解非线性方程组估计重建几何参数的最优解.计算机模拟结果表明,在参数向量初始值接近于真值的情况下,估计所得参数值有较好的精度和重复性.利用此方法估计所得实际扫描系统的几何参数值进行三维重建,也得到了很好的重建结果.

Abstract: The accuracy of reconstructing geometrical parameters is precisely controlled in three-dimensional computed tomography. Because in practical X-ray imaging system, they can’t be measured through direct methods, how to ensure their accuracy becomes the spiny problem. The non-linear least square estimation of three-dimensional reconstructing geometrical parameters based onFeldkamp-type algorithm is introduced. According to the rule that the projection address of a particle in imaging space is as the same as the centroids of its projection. The parameters’ optimal value is estimated through calculating centroids of the measured projections of a point source (or an object close to a point source) and solving non-linear equation sets. Computer simulation proves that when the initial value of the parameters are close to their true value, the estimating results are satisfying and of good repetition. In addition, the parameters’ optimal value of the practical testing system estimated by this method is applied to image reconstruction, and the satisfying results are also obtained.

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