CT系统参数标定及成像

Parameter Calibration and Imaging of CT System

本文主要讨论2017年全国大学生数学建模竞赛A题的CT系统参数标定及成像问题.首先,利用Radon变换滤波反投影,建立了CT图像重构模型,利用标定模板的吸收率推导出参数CT系统的中心位置、探测器单元距离和X射线方向,进而得到成像位置校正参数.然后,利用Beer-Lambert定律得到接收信息,衰减系数,吸收率之间的关系并对赛题附件所给两个未知物体的接收信息进行重构和校正,利用中值滤波和Wiener滤波得到清晰的图像和指定位置的吸收率.最后,讨论了现行的参数标定模板的准确性问题及误差产生原因,提出新的参数标定模板,并进行了不同条件下的重构实验,验证新模板的有效性.

The Problem A of CUMCM 2017, Calibration and hnaging of CT system parameters, is discussed in this paper. Firstly, the CT image reconstruction model is established by using Radon transtorm and filtering back-projection. The central position of the parameter CT system, the distance of the detector unit and the directions of X-ray are derived from the absorptivity of the calibration template. Theretore, the imaging position correction parameters are obtained. Secondly, by using Beer-Lambert＇s law, the relationship among the received intormation, attenuation coefficient and absorption rate are obtained, which can be used to reconstruct and correct the receiving intormation of two unknown objects given in the attachment of the match question. Median filtering and Wiener filtering are applied in getting a clear image and the absorption rate of the position. Finally, the precision of the current parameter calibration template and the causes of errors are discussed. A new template for parameter calibration is proposed. The reconstruction experiments under different conditions are carried out to verily the effectiveness of the new template.