中文摘要：

摘要：提出了一种新的基于正交多项式展开的CT三维投影数据重建算法。首先利用正交多项式空间中的一组正交基对定义在圆柱域的三维密度函数进行傅里叶展开，推导函数与投影数据的部分和关系；然后使用高斯求积公式对上述部分和表达式积分，得到针对三维投影数据的重建算法。在此基础上引入快速傅里叶变换，以提升算法整体的重建效率和数值计算的可行性。实验结果表明：本文提出的算法能够很好地对CT三维投影数据进行重建，且重建效率较高。

英文摘要：

A new method based on orthogonal polynomial expansion is proposed to reconstruct 3D CT projection in this paper. Firstly, a set of orthogonal bases in orthogonal space are used to expand the density function defined in cylindrical domain. The relation between density function and projection data is derived. And then, Gaussian quadrature rule is utilized to integral the above partial sum, which attains the reconstruction algorithm for 3D-projection data. Furthermore, the fast Fourier transform is introduced to improve the efficiency and feasibility of the proposed algorithm. Experiment results show that the algorithm proposed in this work can effectively handle the reconstruction task of 3D- projection with higher efficiency.