Compressed sensing (CS) significantly accelerates magnetic resonance imaging (MRI) by allowing the exact reconstruction of image from highly undersampling k-space data. In this process, the high sparsity obtained by the learned dictionary and exploitation of correlation among patches are essential to the reconstructed image quality. In this paper, by a use of these two aspects, we propose a novel CS-MRI model based on analysis dictionary learning and manifold structure regularization (ADMS). Furthermore, a proper tight frame constraint is used to obtain an effective overcomplete analysis dictionary with a high sparsifying capacity. The constructed manifold structure regularization nonuniformly enforces the correlation of each group formed by similar patches, which is more consistent with the diverse nonlocal similarity in realistic images. The proposed model is efficiently solved by the alternating direction method of multipliers (ADMM), in which the fast algorithm for each sub-problem is separately developed. The experimental results demonstrate that main components in the proposed method contribute to the final reconstruction performance and the effectiveness of the proposed model.

中文翻译：

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基于分析字典学习和流形结构正则化的CS-MRI重建。

压缩传感（CS）通过允许从高度欠采样的k空间数据中精确重建图像，极大地加快了磁共振成像（MRI）的速度。在此过程中，通过学习的字典获得的高稀疏性以及利用补丁之间的相关性对于重建的图像质量至关重要。在本文中，利用这两个方面，我们提出了一种基于分析字典学习和流形结构正则化（ADMS）的新型CS-MRI模型。此外，使用适当的紧框架约束来获得具有高稀疏化能力的有效的不完全分析字典。构造的流形结构正则化非均匀地增强了由相似补丁形成的每个组的相关性，这与现实图像中的各种非局部相似性更加一致。所提出的模型通过乘数交替方向方法（ADMM）有效地求解，其中分别开发了每个子问题的快速算法。实验结果表明，所提出的方法的主要成分有助于最终的重建性能和所提出的模型的有效性。