中文摘要：

计算机断层成像（computed tomography,CT）技术在医学和工业无损检测中都具有非常广泛的应用，CT重建算法是其中的核心，而不完全角度重建问题则是实际应用中重建算法研究领域的一个热点和难点问题．近年来，随着稀疏优化理论与算法的飞速发展，基于稀疏优化的重建算法已经在不完全角度重建问题中得到了较广泛的应用，且表现出了良好的精度与速度性能．本文首先对稀疏优化的基本理论结论与常用算法进行了介绍：而后对稀疏优化理论在CT图像不完全角度重建中的应用进行归纳，分类介绍了其主要研究成果及稀疏优化所发挥的作用；最后对基于稀疏优化的不完全角度重建研究进行了展望．

英文摘要：

Computed tomography （CT） is a technology widely used in medicine and industrial non-destructive testing, and the image reconstruction algorithm is a core technology of CT. Now, the image reconstruction from few-view projections is a hot point in the study of reconstruction algorithm. With the advancements in theories and algorithms, the sparse optimization has recently been applied to few-view reconstruction for CT image, and shown to have a good performance in both accuracy and speed. In this paper, basic conclusions and classical algorithms in sparse optimization are introduced. Furthermore, the spare optimization based few-view reconstruction algorithms for CT image, in particular the main results and the values of spare optimization, are summarized. Finally, the future research direction of sparse optimization based few-view reconstruction for CT image is discussed.