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Total variation (TV) regularization is a technique commonly utilized to promote sparsity of image in gradient domain. In this article, we address the problem of MR brain image reconstruction from highly undersampled Fourier measurements. We define the Moreau enhanced function of L 1 norm, and introduce the minmax-concave TV (MCTV) penalty as a regularization term for MR brain image reconstruction. MCTV strongly induces the sparsity in gradient domain, and fits the frame of fast algorithms (eg, ADMM) for solving optimization problems. Although MCTV is non-convex, the cost function in each iteration step can maintain convexity by specifying the relative nonconvexity parameter properly. Experimental results demonstrate the superior performance of the proposed method in comparison with standard TV as well as nonlocal TV minimization method, which suggests that MCTV may have promising applications in the field of neuroscience in the future. K E Y W O R D S brain image reconstruction, magnetic resonance imaging, non-convex regularization, total variation Int J Imaging Syst Technol. 2018;1-8. wileyonlinelibrary.com/journal/ima V C 2017 Wiley Periodicals, Inc. | 1

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