This paper introduces an efficient algorithm for the compressed MR image reconstruction problem, which is formulated as the minimization of a linear combination of three terms corresponding to a least square data fitting, nonlocal total variation (NLTV) and wavelet sparsity regularization. In our method, the original minimization problem is decomposed into wavelet sparsity and NLTV norm regularization subproblems respectively. Then, these two subproblems are efficiently solved by existing techniques. Finally, the reconstructed image is obtained from the weighted average of solutions from two subproblems in an iterative framework. Experiments with improved performance over previous methods demonstrate the superior performance of the proposed algorithm for compressed MR image reconstruction.
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