21世纪以来，针对民航飞机和陆地公共交通系统的恐怖袭击事件连续发生，公共安全成为世界各国共同关心的课题。隐藏在行李中的爆炸物是公共安全的主要威胁之一，具有材料识别能力的双能X射线成像设备则是检测爆炸物的有效手段。本文围绕安全检查领域的双能X射线成像设备的材料识别算法展开。 对于双能成像，透视扫描是目前的主流成像方式，但是现有的材料识别算法精度较低，不能满足需求。双能CT成像则是技术发展方向，然而在文献中尚未发现满足实用要求的材料识别算法。本论文从成像原理出发，研究了适用于双能透视成像和双能CT成像的材料识别算法，并且在实验系统上验证了算法的可行性。论文所做的研究工作以及取得的成果可概括如下。 首先，推导了双能透视成像的双能曲线模型，利用模型得到了查找表形式的原子序数计算方法。双能曲线模型在理论上能够精确计算原子序数，在实验中精度能够满足材料识别要求。将双能曲线模型用于对双能透视系统的材料区分能力进行定量评价，发现了材料区分度的变化规律。还建立数学模型对双能系统的铜滤波片厚度进行了优化设计，并利用实验证实了优化结果。 其次，将基材料分解模型引入双能CT安全检查领域，揭示了模型精度随着原子序数的变化规律，推导了从基材料分解系数求解原子序数和电子密度的公式，为双能CT成像中原子序数和电子密度的重建打下基础。 然后，关于圆轨道双能CT成像，提出了基于能谱估计的双能CT重建方法。该方法的关键问题是确定系统能谱和求解双能方程组。论文提出了从透射测量数据估计系统能谱的EM迭代算法，并设计了双能方程组的优化解法，然后利用实验证明了基于能谱估计的双能CT重建方法能够满足液体安全检查的要求。 最后，提出了大螺距螺旋双能CT重建方法。该方法的关键问题是双能分解和大螺距重建。关于双能分解，引入有理函数近似方法取得了优于传统方法的分解精度；关于大螺距重建，从减少投影数据不一致性的角度提出了最少数据重建算法，在减轻结构伪影和提高重建值准确性方面比常规算法更优。实验证明所提出的大螺距螺旋双能CT重建方法能够满足行李安全检查的需求。

Since the 21st century, terrorist attacks on civil aviation and ground public traffic system occurred frequently in the world. Public security has become a common concern among countries. Explosives hidden in luggage are one of the major threats to public safety. Dual energy X-ray imaging technique able to discriminate materials is an effective solution for explosive detection. The main work of this dissertation is concentrated on material recognition methods for dual energy X-ray imaging systems applied in security inspection. As to dual energy imaging, transmission imaging is the dominant modality, but the existing material recognition algorithms cannot meet the accuracy requirement. Dual energy computed tomography is a promising direction. However, existing material recognition methods in this research field are not practical. Basing on the fundamental of dual energy imaging, we investigated the material recognition methods for both dual energy transmission imaging and CT imaging, and validated the methods on our experimental systems. The research work and contributions of the dissertation can be summarized as follows. Firstly, we theorized the dual energy curve model for dual energy transmission imaging system, and based on the model developed a method to calculate atomic number using a lookup table. This method is exact in theory and provides sufficient accuracy for material recognition in experiments. By applying this model to the quantitative performance evaluation of the material classification with a dual energy system, we can reveal the regularity of the classification ability. Moreover, we established a mathematical model to optimize the thickness of a copper filter in the experimental system, and validated the result in experiments. Secondly, we introduced the basis material decomposition model into a dual energy CT for security inspection and discovered the rule of its accuracy in variation. We derived formulas for computing atomic number and electron density from basis material decomposition coefficients. This work acted as a theoretical foundation for dual energy CT reconstruction of both atomic number and electron density. Thirdly, about circular trajectory dual energy CT imaging, we proposed an image reconstruction method based on spectra estimation. The key of this method lies in determining system spectra and solving dual energy equation set. We derived an EM method for estimating the system spectra from transmission measurements, and designed an optimized method to solve the equation set. Experimental studies showed that the proposed dual energy reconstruction method fulfilled the requirements for liquid security inspection. Finally, we proposed an image reconstruction method for high pitch helical dual energy CT. The key of this method lies in dual energy projection decomposition and high pitch helical CT reconstruction. We introduced the rational function approximation method into dual energy projection decomposition. It gives a better precision than conventional methods. For high pitch reconstruction, we proposed a minimal data reconstruction method based on reducing the inconsistency in projection data to minimum. It is superior to existing methods in removing structural artifacts and improving reconstruction precision. Experimental tests of the overall reconstruction method showed its ability for detecting explosives in passenger luggage.