While low-rank matrix prior has been exploited in dynamic MR image reconstruction and has obtained satisfying performance, tensor low-rank models have recently emerged as powerful alternative representations for three-dimensional dynamic MR datasets. In this paper, we introduce a novel deep unrolling network for dynamic MRI, namely the learned transform-based tensor low-rank network (LT$^2$LR-Net). First, we generalize the tensor singular value decomposition (t-SVD) into an arbitrary unitary transform-based version and subsequently propose the novel transformed tensor nuclear norm (TTNN). Then, we design a novel TTNN-based iterative optimization algorithm based on the alternating direction method of multipliers (ADMM) to exploit the tensor low-rank prior in the transformed domain. The corresponding iterative steps are unrolled into the proposed LT$^2$LR-Net, where the convolutional neural network (CNN) is incorporated to adaptively learn the transformation from the dynamic MR dataset for more robust and accurate tensor low-rank representations. Experimental results on the cardiac cine MR dataset demonstrate that the proposed framework can provide improved recovery results compared with the state-of-the-art methods.

翻译：尽管低秩矩阵先验已被用于动态磁共振图像重建并取得了令人满意的性能，但张量低秩模型最近作为三维动态磁共振数据集的强大替代表示方式出现。本文提出了一种新颖的深度展开网络用于动态磁共振成像，即基于学习变换的张量低秩网络（LT$^2$LR-Net）。首先，我们将张量奇异值分解（t-SVD）推广至任意酉变换版本，并随后提出新颖的变换张量核范数（TTNN）。接着，基于交替方向乘子法（ADMM），我们设计了一种新颖的基于TTNN的迭代优化算法，以利用变换域中的张量低秩先验。相应的迭代步骤被展开成所提出的LT$^2$LR-Net，其中卷积神经网络（CNN）被引入以从动态磁共振数据集中自适应学习变换，从而实现更鲁棒且更准确的张量低秩表示。在心脏电影磁共振数据集上的实验结果表明，与最先进方法相比，所提出的框架能够提供更优的重建结果。