Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations

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.