Dynamic MRI Reconstruction Combining Tensor Nuclear Norm and Casorati Matrix Nuclear Norm

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 novel dMRI reconstruction method combining TNN and Casorati MNN, which we term as TMNN. Moreover, we convert the the TMNN dMRI reconstruction problem into a simple tensor completion problem, which can be efficiently solved by the alternating direction method of multipliers (ADMM).