  In dynamic magnetic resonance (MR) imaging, low-rank plus sparse (L+S)
decomposition, or robust principal component analysis (PCA), has achieved
stunning performance. However, the selection of the parameters of L+S is
empirical, and the acceleration rate is limited, which are common failings of
iterative compressed sensing MR imaging (CS-MRI) reconstruction methods. Many
deep learning approaches have been proposed to address these issues, but few of
them use a low-rank prior. In this paper, a model-based low-rank plus sparse
network, dubbed L+S-Net, is proposed for dynamic MR reconstruction. In
particular, we use an alternating linearized minimization method to solve the
optimization problem with low-rank and sparse regularization. Learned soft
singular value thresholding is introduced to ensure the clear separation of the
L component and S component. Then, the iterative steps are unrolled into a
network in which the regularization parameters are learnable. We prove that the
proposed L+S-Net achieves global convergence under two standard assumptions.
Experiments on retrospective and prospective cardiac cine datasets show that
the proposed model outperforms state-of-the-art CS and existing deep learning
methods and has great potential for extremely high acceleration factors (up to
24x).
