Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning.
Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning.
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DOI：
10.1109/msp.2019.2950432
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发表时间：
2020-01
影响因子：
14.9
通讯作者：
Ye JC
中科院分区：
文献类型：
--
作者：
Jacob M;Mani MP;Ye JC
在这次调查中，我们提供了一个详细的审查最近的进展，在恢复连续域多维信号从他们的几个非均匀（多通道）测量使用结构化的低秩矩阵完成制定。这个框架的核心是紧凑性之间的基本二元性（例如，稀疏性）和结构化矩阵的秩，结构化矩阵的条目是信号的函数。该属性使得信号恢复能够重新表述为低秩结构化矩阵完成，这具有性能保证。我们还将审查快速算法，其复杂性与当前的压缩感知方法相当，这使得该框架能够应用于大规模磁共振（MR）恢复问题。显着的灵活性，制定可用于利用信号的属性，难以捕捉当前的稀疏和低秩优化策略。我们证明了该框架在广泛的MR成像（MRI）应用中的实用性，包括高度加速成像、免校准采集、MR伪影校正和非门控动态MRI。
In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI.
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影响因子：
3.3
作者：
Haldar JP;Zhuo J
通讯作者：
Zhuo J
影响因子：
5.4
作者：
Ongie G;Jacob M
通讯作者：
Jacob M
影响因子：
2.1
作者：
Ongie G;Jacob M
通讯作者：
Jacob M
影响因子：
3
作者：
Candes, Emmanuel J.;Fernandez-Granda, Carlos
通讯作者：
Fernandez-Granda, Carlos
影响因子：
3.3
作者：
Jiang, Wenwen;Larson, Peder E. Z.;Lustig, Michael
通讯作者：
Lustig, Michael