基于优化的CT系统标定与滤波反投影图像重建

摘要

该文建立了CT系统标定模型和CT系统重建模型, 分析了标定模型的精度和稳定性, 并设计了精度和稳定性更高的标定模板及对应的标定模型.针对CT系统标定问题, 结合几何知识及接收信息建立方程组联立求解, 计算出增益系数、探测器单元间距和各方向上的平行射线方程, 从而建立优化模型并利用遗传算法得到旋转中心坐标.针对CT图像重建问题, 首先推导了衰减系数与像素值的关系, 然后采用各种滤波器进行滤波反投影重建.最后通过计算机正向模拟和反向求解分析了标定模板的精度和稳定性, 设计了稳定性高的长方形-圆模板和精度高的长方形-椭圆-圆模板.%In this paper, the CT system calibration model and the CT system reconstruction model are established.The accuracy and stability of the calibration model are analyzed, and the calibration template with higher accuracy and stability and the corresponding calibration model are designed.For the calibration problem of CT system, combined with geometric knowledge and receiving information, the equations are solved jointly.The gain coefficient, the detector cell spacing and parallel ray equations in all directions are calculated to establish an optimization model and the rotation center coordinates are obtained by the genetic algorithm.For the CT image reconstruction problem, the relationship between the attenuation coefficient and the pixel value is first deduced, and then the filter is used for back-projection reconstruction.Finally, the accuracy and stability of the calibration template are analyzed by computer forward simulation and reverse solution.Finally, a rectangular-circle template with high stability and a rectangular-oval-circle template with high precision are designed.