  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.
