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Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approaches lack the modeling of physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier (PF), regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k -space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k -space data), including transform sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k -space data accuracy. Finally, ablation experiments show that the proposed method can characterize the physical priors of MR images well. Additionally, experiments show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and is even competitive against supervised-trained deep learning methods in PF and regular undersampling reconstruction. • A physical prior-driven untrained neural network was proposed for MRI reconstruction. • The accuracy of the proposed model's MRI reconstruction was analyzed. • Experimental results confirmed model's superiority in MRI reconstruction. [ABSTRACT FROM AUTHOR]

• A model-based unrolled low-rank plus sparse network (L+S-Net) for dynamic MR reconstruction is proposed. • A learned singular value thresholding (LSVT) was introduced to exploit the deep low rank prior in dynamic MR. • The iterative steps are unrolled into a network whose regularization parameters are learned during training instead of the empirical selection. • The convergence analysis guarantees the performance of the reconstruction theoretically. • Retrospective and prospective study on single-coil/multi-coil datasets show that the L+S-Net can improve the reconstruction result both qualitatively and quantitatively. [Display omitted] 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 24 ×). [ABSTRACT FROM AUTHOR]