Abstract: The new image reconstruction algorithm remains one of the hot problems in the current research of computed tomography(CT),among which the reconstruction algorithm with limited views is a difficult problem in practice.Recently,a sparse signal recovery theory was proposed by Terence Tao and his colleagues,which may give a strategy for solving this problem.We introduced this theory and presented some primary simulated results in this paper.The realization of the strategy is significant in some special applications for cone beam CT imaging,which will be a new direction in this field and will greatly influence on this field.