基于加权TV正则化的X射线CT系统能谱估计方法

在CT硬化伪影校正、双能CT图像重建以及CT辐射剂量计算等实际应用中，X射线的能谱信息具有重要的作用。然而，由于透射测量方程组系数矩阵的病态性、X光子的统计涨落和噪声的干扰，使得EM等能谱估计方法难以获得较精细的能谱刻画。针对该问题，提出一种基于加权TV正则化的X射线CT系统能谱估计方法。首先采用能谱能量范围内带有不同K-edge的材料作为体模以降低投影测量方程之间的相关性。然后，利用CT成像系统的几何参数来获取投影测量数据所对应的准确透射长度信息来减小投影方程的测量误差。最后，综合利用透射衰减测量数据的保真性、轫致辐射能谱部分的连续性、特征辐射能谱部分的离散性、能谱的非负性和归一性以及平均有效衰减系数等信息，使用加权TV正则化方法建立目标函数，利用正则化理论中的L曲线准则通过黄金分割参数搜索策略求得最优正则化参数及对应的能谱估计结果。分别通过不同统计波动模型下的仿真能谱和实际测量数据对算法性能进行了验证，结果表明该方法与EM等方法相比，不受初始能谱的影响，有效提高了能谱估计结果的稳定性和准确性。

X-Ray CT Energy Spectrum Estimation Algorithm Based on Weighted TV Normalization

In practical applications ,such as CT hardening artifacts correction ,dual energy CT image reconstruction and CT radi-ation dose calculation ,X-ray energy spectrum information plays an important role .However ,due to high ill-condition of system equations of transmission measurement data ,statistical fluctuations of X-ray quantum and noise pollution ,it is hard to get accu-rate spectrum estimation using existing methods such as EM method .In this paper ,an X-ray energy spectrum estimation method based on adaptive TV normalization is proposed .First ,the phantom materials with different K-edge in energy range of spectrum are used to reduce the correlation between the projection measurement equations .Then ,the geometric parameters of CT imaging system are used to obtain the accurate transmission length information corresponding to the projection measurement data to re-duce the measurement error of the projection equations .Finally ,with comprehensive utilization of transmission attenuation measurement data fidelity ,continuity of bremsstrahlung emission energy spectrum ,discreteness of characteristic radiation energy spectrum ,non-negativity and normalization of energy spectrum ,average effective attenuation coefficient and other information ,objective function was established using weighted TV normalization method .The parameter in normalization model was opti-mized with L curve guideline and searched in accordance with golden section strategy to get the best estimation result .Experi-mental results demonstrate that the stability and accuracy of X-ray energy spectrum estimation using the proposed method are significantly improved compared to the EM method .