Magnetic resonance imaging (MRI) reconstruction model based on total variation (TV) regularization can deal with problems such as incomplete reconstruction, blurred boundary, and residual noise. In this article, a non‐convex isotropic TV regularization reconstruction model is proposed to overcome the drawback. Moreau envelope and minmax‐concave penalty are firstly used to construct the non‐convex regularization of L₂ norm, then it is applied into the TV regularization to construct the sparse reconstruction model. The proposed model can extract the edge contour of the target effectively since it can avoid the underestimation of larger nonzero elements in convex regularization. In addition, the global convexity of the cost function can be guaranteed under certain conditions. Then, an efficient algorithm such as alternating direction method of multipliers is proposed to solve the new cost function. Experimental results show that, compared with several typical image reconstruction methods, the proposed model performs better. Both the relative error and the peak signal‐to‐noise ratio are significantly improved, and the reconstructed images also show better visual effects. The competitive experimental results indicate that the proposed approach is not limited to MRI reconstruction, but it is general enough to be used in other fields with natural images.

中文翻译：

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通过非凸总变化正则化进行磁共振成像重建

基于总变化（TV）正则化的磁共振成像（MRI）重建模型可以处理诸如重建不完全，边界模糊和残留噪声之类的问题。本文提出了一种非凸各向同性电视正则化重构模型来克服这一缺点。首先使用Moreau包络和最小凹凹罚分构造L ₂的非凸正则化规范，然后将其应用于电视正则化以构建稀疏重建模型。该模型可以避免凸正则化中较大的非零元素的低估，因此可以有效地提取目标的边缘轮廓。另外，在某些条件下可以保证成本函数的全局凸性。然后，提出了一种有效的算法，例如乘法器的交替方向法，来求解新的成本函数。实验结果表明，与几种典型的图像重建方法相比，该模型具有更好的性能。相对误差和峰值信噪比均得到显着改善，并且重建的图像也显示出更好的视觉效果。