微分相位衬度计算机层析成像法(DPC-CT)是一种新的X射线无损检测方法。与传统方法相比，该方法在检测弱吸收物质时优势明显。但DPC-CT技术需要进行多次扫描后才能获取足够的样品信息，这必将导致很长的辐射时间和巨大的辐射剂量。因此，研究在稀疏角度条件下的DPC-PC重建算法就显得尤为重要。分析了DPC-CT的特点，在凸集投影(POCS)的理论框架下，将L1范数、曲波系数约束和经典的代数迭代算法(ART)相结合提出了一种适合DPC-CT的重建算法。数值模拟和实验的结果表明，该方法可以根据少量投影数据获得较好的重建结果。

Differential phase contrast computed tomography (DPC-CT) is a novel X-ray inspection method which has obvious advantage in detecting weak absorption substance compared with conventional CT reconstruction methods. However, DPC-CT usually need to scan many times in order to obtain enough refraction angle information, which leads to unacceptably long exposure time and huge X-ray doses. Thus, the study of sparse angular DPC-CT reconstruction algorithm is particularly important. After analyzing the characteristics of the DPC-CT. Based on the theoretical framework of projection on convex set (POCS), a reconstruction algorithm for DPC-CT is proposed by combining L1 norm, curvelet coefficient constraint and dassical algebra reconstruction technique (ART). The numerical simulation and experimental results show that the proposed algorithm can significantly improve the image quality of the sparse angular DPC-CT reconstructions.