Abstract: We briefly recall previous literature about the few-view projection reconstruction problems.The few-view projection problem belongs to the uncompleted data reconstruction,which means the projection number is much fewer than common conditions,such as one tenth,or twentieth.Because of the similarity,some of the ideas are from the reconstruction algorithms of the limited angle problems.There are mainly two thoughts of the reconstruction: one is sinogram recovery methods,such as the angular interpolation,transform-based iterative-analytic reconstructions;the other is image recovery methods,such as reconstruction methods incorporating a priori information,TV constraint.