An efficient algorithm for dynamic MRI using low-rank and total variation regularizations

In this paper, we propose an efficient algorithm for dynamic magnetic resonance (MR) image reconstruction. With the total variation (TV) and the nuclear norm (NN) regularization, the TVNNR model can utilize both spatial and temporal redundancy in dynamic MR images. Such prior knowledge can help model dynamic MRI data significantly better than a low-rank or a sparse model alone. However, it is very challenging to efficiently minimize the energy function due to the non-smoothness and non-separability of both TV and NN terms. To address this issue, we propose an efficient algorithm by solving a primal-dual form of the original problem. We theoretically prove that the proposed algorithm achieves a convergence rate of O(1/N) for N iterations. In comparison with state-of-the-art methods, extensive experiments on single-coil and multi-coil dynamic MR data demonstrate the superior performance of the proposed method in terms of both reconstruction accuracy and time complexity.