Dynamic MRI reconstruction using low-rank and 3D sparsifying transform with separation of background and dynamic components

Dynamic magnetic resonance imaging (MRI) is an important auxiliary diagnostic method, and higher resolution of images is more conducive to the doctor to diagnose. In this paper, we extend a method which is referred to as robust principal component analysis (RPCA) to reconstruct dynamic magnetic resonance data from under-sampled measurements based on the low-rank plus sparse decomposition model. We consider the dynamic MRI as the sum of the background and the dynamic components, where the background is enforced low-rank by a non-convex function and a 3D sparsifying transform is used to enforce sparsity in the dynamic components. The proposed optimization problem is solved based on variable splitting and alternative optimization. The results of the in-vivo dynamic cardiac dataset show the proposed method achieves superior reconstruction quality, compared to the state-of-the-art reconstruction methods.