Compressive sensing (CS) theory has great potential for reconstructing CT images from sparse-views projection data. Currently, total variation (TV-) based CT reconstruction method is a hot research point in medical CT field, which uses the gradient operator as the sparse representation approach during the iteration process. However, the images reconstructed by this method often suffer the smoothing problem; to improve the quality of reconstructed images, this paper proposed a hybrid reconstruction method combining TV and non-aliasing Contourlet transform (NACT) and using the Split-Bregman method to solve the optimization problem. Finally, the simulation results show that the proposed algorithm can reconstruct high-quality CT images from few-views projection using less iteration numbers, which is more effective in suppressing noise and artefacts than algebraic reconstruction technique (ART) and TV-based reconstruction method.

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