基于二次有理分式拟合多能投影曲线的X射线能谱估计方法

在X射线计算机断层（CT）成像领域，多种应用需要准确的X射线能谱信息，包括能谱CT图像重建、CT图像硬化校正、CT图像的定量分析等.然而，由于CT系统中X光机发出的射线流强很大，X射线能谱一般难以直接测量，更为常用的方法是利用不同厚度模体的投影数据，间接估计能谱.该类方法将能谱估计问题转化为一组病态线性方程组的求解问题.为了获得较为准确的X射线能谱，通常需要测量多组投影数据，工作量大.针对该问题，本文提出一种新的X射线能谱估计方法.该方法利用二次有理分式拟合多能投影曲线，然后利用多能投影曲线上的采样点间接估计X射线能谱.由于二次有理分式参数少，因此该方法仅需少量的测量点即可拟合出高精度的多能投影曲线.实验表明：本文方法仅需要3个测量点就可以达到传统方法使用十几个测量点估计的X射线能谱的精度，显著减少了采样数量，进而减少能谱估计的工作量.仿真和实采数据都验证了方法的有效性.

X-Ray Spectrum Estimation Method Based on Polychromatic Projection Curve Fitting with Quadratic Rational Fraction

Knowledge of X-ray spectrum is essential in many applications of X-ray computed tomography (CT),such as spectral CT imaging,beam hardening correction,quantitative analysis of CT images,etc.But the spectrum of an X-ray source is hard to measure with X-ray spectrometer directly due to strong X-ray flux emitted.Other kind of attractive methods are indirect,which estimate the x-ray spectrum from a set of projection data of phantoms with different thicknesses.In indirect methods,the spectrum estimation problem is boiled down to a set of ill conditioned linear equations.To acquire accurate spectrum,a large number of measurements are required,which needs heavy workload.To overcome the abovementioned obstacle,we propose a novel X-ray spectrum estimation method that first fits the polychromatic projection curve with quadratic rational fraction,and then estimate the X-ray spectrum from the sampling points of the fitted curve.As a quadratic rational fraction includes only three parameters,only a few measurements are needed to get an accurate fitting.Numerical experiments show that the accuracy of the X-ray spectrum estimated through the proposed method with three measurements is commensurate to that estimated with tradition method from over a dozen of measurements.Therefore,the proposed method lessens the workloads effectively.