关键词: 核磁共振成像, 全变差正则, Moreau包络, 最小最大凹罚函数, 交替方向乘子法

Abstract: To solve the problems of incomplete reconstruction, blurred boundary and residual noise in Magnetic Resonance (MR) image reconstruction, a non-convex total variation regularization reconstruction model based on L₂ regularization was proposed. First, Moreau envelope and minmax-concave penalty function were used to construct the non-convex regularization of L₂ norm, then it was applied into the total variation regularization to construct the sparse reconstruction model based on the isotropic non-convex total variation regularization. The proposed non-convex regularization was able to effectively avoid the underestimation of larger non-zero elements in convex regularization, so as to reconstruct the edge contour of the target more effectively. At the same time, it was able to guarantee the global convexity of objective function under certain conditions. Therefore, Alternating Direction Method of Multipliers (ADMM) was able to be used to solve the model. Simulation experiments were carried out to reconstruct several MR images under different sampling templates and sampling rates. Experimental results show that compared with several typical image reconstruction methods, the proposed model has better performance and lower relative error, its Peak Signal-to-Noise Ratio (PSNR) is significantly improved, which is 4 dB higher than that of traditional reconstruction method based on the non-convex regularization of L₁ norm; in addition, the visual effects of the reconstructed images are promoted significantly, effectively maintaining the edge details of the original images.

Key words: Magnetic Resonance Imaging (MRI), total variation regularization, Moreau envelope, minmax-concave penalty function, Alternating Direction Method of Multipliers (ADMM)