Compressive sensing (CS) is an effective method for reconstructing magnetic resonance imaging (MRI) image from under-determined linear system (ULS). However, how to improve the accuracy of MRI image reconstructed by CS is still a serious problem, especially in noisy conditions. To solve this problem, in this paper, we propose a novel approach, dubbed as regularized maximum entropy function (RMEF) minimization algorithm. Specifically, motivated by the entropy function in information theory, we propose a maximum entropy function (MEF) to approximate Lq-norm (0 < q < 1) as sparsity promoting objectives, and then the regularization mechanism for improving the de-noising performance is adopted. Combining the above two ideas, a new objective function of RMEF method is proposed, and the global minimum is iteratively solved. We further analyze the convergence to verify the robustness of the RMEF algorithm. Experiments demonstrate the state-of-the-art performances of the proposed RMEF algorithm and show that the RMEF achieves higher PSNR and SSIM than other widely-adopted methods in MRI image recovery.
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