  Low-rank tensor models have been applied in accelerating dynamic magnetic
resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD
has been proposed and applied to tensor completion. Inspired by the different
properties of the tensor nuclear norm (TNN) and the Casorati matrix nuclear
norm (MNN), we introduce a combined TNN and Casorati MNN regularizations
framework to reconstruct dMRI, which we term as TMNN. The proposed method
simultaneously exploits the spatial structure and the temporal correlation of
the dynamic MR data. The optimization problem can be efficiently solved by the
alternating direction method of multipliers (ADMM). In order to further improve
the computational efficiency, we develop a fast algorithm under the Cartesian
sampling scenario. Numerical experiments based on cardiac cine MRI and
perfusion MRI data demonstrate the performance improvement over the traditional
Casorati nuclear norm regularization method.

Image and Video Processing;Computer Vision and Pattern Recognition;Machine Learning