An efficient algorithm for dynamic MRI using low‐rank and total variation regularizations
An efficient algorithm for dynamic MRI using low‐rank and total variation regularizations
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DOI：
10.1016/j.media.2017.11.003
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发表时间：
2018-02
影响因子：
10.9
通讯作者：
Jiawen Yao;Zheng Xu;Xiaolei Huang;Junzhou Huang
中科院分区：
文献类型：
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作者：
Jiawen Yao;Zheng Xu;Xiaolei Huang;Junzhou Huang
在本文中，我们提出了一种有效的算法，用于动态磁共振（MR）图像重建。TVNNR模型通过总变分（TV）和核范数（NN）正则化，可以同时利用动态MR图像的空间和时间冗余。这样的先验知识可以帮助对动态MRI数据进行建模，明显优于单独的低秩或稀疏模型。然而，由于TV和NN项的非光滑性和不可分离性，有效地最小化能量函数是非常具有挑战性的。为了解决这个问题，我们提出了一个有效的算法，通过解决原问题的原始对偶形式。我们从理论上证明了该算法实现了N次迭代的O（1/N）的收敛速度。在单线圈和多线圈动态MR数据上的大量实验表明，与现有方法相比，该方法在重建精度和时间复杂度方面具有上级性能。
In this paper, we propose an efficient algorithm for dynamic magnetic resonance (MR) image reconstruction. With the total variation (TV) and the nuclear norm (NN) regularization, the TVNNR model can utilize both spatial and temporal redundancy in dynamic MR images. Such prior knowledge can help model dynamic MRI data significantly better than a low-rank or a sparse model alone. However, it is very challenging to efficiently minimize the energy function due to the non-smoothness and non-separability of both TV and NN terms. To address this issue, we propose an efficient algorithm by solving a primal-dual form of the original problem. We theoretically prove that the proposed algorithm achieves a convergence rate of O (1/N) for N iterations. In comparison with state-of-the-art methods, extensive experiments on single-coil and multi-coil dynamic MR data demonstrate the superior performance of the proposed method in terms of both reconstruction accuracy and time complexity.