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The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography (CT) reconstruction. A method employing the image gradient sparsity is often used to reduce the sampling rate and is shown to remove the unwanted artifacts while preserve sharp edges, but may cause blocky or patchy artifacts. To eliminate this drawback, we propose a novel sparsity exploitation-based model for CT image reconstruction. In the presented model, the sparse representation and sparsity exploitation of both gradient and nonlocal gradient are investigated. The new model is shown to offer the potential for better results by introducing a similarity prior information of the image structure. Then, an effective alteating direction minimization algorithm is developed to optimize the objective function with a robust convergence result. Qualitative and quantitative evaluations have been carried out both on the simulation and real data in terms of accuracy and resolution properties. The results indicate that the proposed method can be applied for achieving better image-quality potential with the theoretically expected detailed feature preservation.