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While the methods exploiting the tensor low-rank prior are booming inhigh-dimensional data processing and have obtained satisfying performance,their applications in dynamic magnetic resonance (MR) image reconstruction arelimited. In this paper, we concentrate on the tensor singular valuedecomposition (t-SVD), which is based on the Fast Fourier Transform (FFT) andonly provides the definite and limited tensor low-rank prior in the FFT domain,heavily reliant upon how closely the data and the FFT domain match up. Bygeneralizing the FFT into an arbitrary unitary transformation of thetransformed t-SVD and proposing the transformed tensor nuclear norm (TTNN), weintroduce a flexible model based on TTNN with the ability to exploit the tensorlow-rank prior of a transformed domain in a larger transformation space andelaborately design an iterative optimization algorithm based on the alternatingdirection method of multipliers (ADMM), which is further unrolled into amodel-based deep unrolling reconstruction network to learn the transformedtensor low-rank prior (T$^2$LR-Net). The convolutional neural network (CNN) isincorporated within the T$^2$LR-Net to learn the best-matched transform fromthe dynamic MR image dataset. The unrolling reconstruction network alsoprovides a new perspective on the low-rank prior utilization by exploiting thelow-rank prior in the CNN-extracted feature domain. Experimental results on twocardiac cine MR datasets demonstrate that the proposed framework can provideimproved recovery results compared with the state-of-the-art optimization-basedand unrolling network-based methods.

T$^2$LR-Net: An Unrolling Reconstruction Network Learning Transformed Tensor Low-Rank prior for Dynamic MR Imaging