Yu Yeyang, Jin Jin, Liu Feng, Crozier Stuart
School of Information Technology and Electrical Engineering, the University of Queensland, St Lucia, Queensland, Australia.
PLoS One. 2014 Jun 5;9(6):e98441. doi: 10.1371/journal.pone.0098441. eCollection 2014.
Compressed Sensing (CS) has been applied in dynamic Magnetic Resonance Imaging (MRI) to accelerate the data acquisition without noticeably degrading the spatial-temporal resolution. A suitable sparsity basis is one of the key components to successful CS applications. Conventionally, a multidimensional dataset in dynamic MRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the image sparsity. Traditional methods typically sparsify the spatial and temporal information independently. In this work, we propose a novel concept of tensor sparsity for the application of CS in dynamic MRI, and present the Higher-order Singular Value Decomposition (HOSVD) as a practical example. Applications presented in the three- and four-dimensional MRI data demonstrate that HOSVD simultaneously exploited the correlations within spatial and temporal dimensions. Validations based on cardiac datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods and, outperformed the conventional sparse recovery methods.
压缩感知（CS）已应用于动态磁共振成像（MRI），以加速数据采集，同时不会显著降低时空分辨率。合适的稀疏基是CS成功应用的关键要素之一。传统上，动态MRI中的多维数据集被视为一系列二维矩阵，然后使用各种矩阵/向量变换来探索图像稀疏性。传统方法通常独立地对空间和时间信息进行稀疏化处理。在这项工作中，我们提出了一种用于CS在动态MRI中应用的张量稀疏性新概念，并给出了高阶奇异值分解（HOSVD）作为一个实际例子。在三维和四维MRI数据中的应用表明，HOSVD同时利用了空间和时间维度内的相关性。基于心脏数据集的验证表明，所提出的方法与低秩矩阵恢复方法具有相当的重建精度，并且优于传统的稀疏恢复方法。
