Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China.
IEEE Trans Med Imaging. 2013 Jul;32(7):1290-301. doi: 10.1109/TMI.2013.2256464. Epub 2013 Apr 2.
In recent years Bregman iterative method (or related augmented Lagrangian method) has shown to be an efficient optimization technique for various inverse problems. In this paper, we propose a two-level Bregman Method with dictionary updating for highly undersampled magnetic resonance (MR) image reconstruction. The outer-level Bregman iterative procedure enforces the sampled k-space data constraints, while the inner-level Bregman method devotes to updating dictionary and sparse representation of small overlapping image patches, emphasizing local structure adaptively. Modified sparse coding stage and simple dictionary updating stage applied in the inner minimization make the whole algorithm converge in a relatively small number of iterations, and enable accurate MR image reconstruction from highly undersampled k-space data. Experimental results on both simulated MR images and real MR data consistently demonstrate that the proposed algorithm can efficiently reconstruct MR images and present advantages over the current state-of-the-art reconstruction approach.
近年来，Bregman 迭代法（或相关的增广拉格朗日法）已被证明是一种用于各种反问题的有效优化技术。在本文中，我们提出了一种用于高欠采样磁共振（MR）图像重建的两级 Bregman 字典更新方法。外循环 Bregman 迭代过程强制满足采样的 k 空间数据约束，而内循环 Bregman 方法致力于更新字典和小重叠图像块的稀疏表示，自适应强调局部结构。应用于内部分解的改进稀疏编码阶段和简单字典更新阶段使整个算法在相对较少的迭代次数内收敛，并能够从高度欠采样的 k 空间数据中准确重建 MR 图像。在模拟 MR 图像和真实 MR 数据上的实验结果一致表明，所提出的算法能够有效地重建 MR 图像，并优于当前最先进的重建方法。
