In this paper, the main problem to be solved is how to achieve magnetic resonance imaging (MRI) accurately and quickly. Previous work has shown that compressive sensing (CS) technology can reconstruct a magnetic resonance (MR) image from only a small number of samples, which significantly reduces MR scanning time. Based on this, an algorithm to improve the accuracy of MRI, called regularized weighting Composite Gaussian smoothed l0-norm minimization (RWCGSL0), is proposed in this paper. Different from previous methods, our algorithm has three influential contributions: (1) a new smoothed Composite Gaussian function (CGF) is proposed to be closer to the l0-norm; (2) a new weighting function is proposed; (3) a new l0 regularized objective function framework is constructed. Furthermore, the optimal solution of this objective function is obtained by penalty decomposition (PD)method. It is experimentally shown that the proposed algorithm outperforms other state-of-the-art CS algorithms in the reconstruction of MR images.
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