中文摘要：

针对Radon投影的计算机断层（Computer Tomography，CT）重建问题，提出了一种新的基于单位圆上正交展开法（Orthogonal Polynomial Expansions on the Disk，0PED）的有限角投影数据快速重建算法。该算法通过求解缺失投影与已知数据分别对应的正弦变换数据集之间所满足的线性方程组，得到完备数据正弦变换数据集的近似值，之后运用快速傅里叶变换（Fast Fourier Transform，FFT）及线性插值算法提高重建速度从而缩短重建时间。分别推导了单、双边投影数据缺失时的快速重建算法并给出了重建结果，实验结果证明，该方法能够有效提高重建效率。

英文摘要：

Based on Orthogonal Polynomial Expansions on the Disk algorithm （OPED）, fast reconstruction method of limited angle Radon projections is proposed to cope with the problem of Computed Tomography （CT） in Radon projections. By solving linear system equations to estimate the missing data, Fast Fourier Transform （FFT） and linear interpolation method are applied to reduce the computation time. Derivations and numerical examples for one-side and both-side limited projection reconstruction are given, respectively. The simulation results show that the proposed method can effectively raise the efficiency of reconstruction.