In order to more effectively represent the higher-order sparse structure of images,a novel compressed sensing (CS) reconstruction algorithm based on the graph sparsity regularization was proposed in this paper.The graph theory method was introduced for describing the dependency of sparse coefficients.First,the nonlocal similarity of images was constrained to be graph-structured sparse.To achieve more efficient sparse representation,the structure of sparse coefficients was simplified from the complete graph structure to a star graph of which the coefficients are only connected with the mean node.Second,for obtaining the adaptive reconstruction,the weighted norm was utilized to reflect the different significances of sparsity coefficients.A numerical optimization algorithm was then proposed to solve the star graph structured reconstruction model by the approximate message passing (AMP) algorithm.Finally,the weight parameters and sparse coefficients were estimated easily by introducing auxiliary variables.Experiments results showed that,compared with several image reconstruction algorithms based on nonlocal sparse models,the proposed method presented competitive results in terms of both objective and subjective quality,which validated the effectiveness of the star graph structured model.
