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.