Dynamic MR image reconstruction based on total generalized variation and low‐rank decomposition

PURPOSE: Propose a novel decomposition-based model employing the total generalized variation (TGV) and the nuclear norm, which can be used in compressed sensing-based dynamic MR reconstructions. THEORY AND METHODS: We employ the nuclear norm to represent the time-coherent background and the spatiotemporal TGV functional for the sparse dynamic component above. We first design an algorithm using the classical first-order primal-dual method for solving the proposed model and then give the norm estimation for the convergence condition. The proposed model is compared with the state-of-the-art methods on different data sets under different sampling schemes and acceleration factors. RESULTS: The proposed model achieves higher SERs and SSIMs than kt-SLR, kt-RPCA, L+S, and ICTGV on cardiac perfusion and breast DCE-MRI data sets under both the pseudoradial and the Cartesian sampling schemes. In addition, the proposed model better suppresses the spatial artifacts and preserves the edges. CONCLUSIONS: The proposed model outperforms the state-of-the-art methods and generates high-quality reconstructions under different sampling schemes and different acceleration factors.