# Deep Low-rank plus Sparse Network for Dynamic MR Imaging

arXiv: https://arxiv.org/abs/2010.13677 · HTML: https://mlsanity.com/paper/2010.13677/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2020.

## Built on by (most cited first, 30 of 32)

- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detection](https://mlsanity.com/paper/2311.00917/) (2023)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Self-Score: Self-Supervised Learning on Score-Based Models for MRI Reconstruction](https://mlsanity.com/paper/2209.00835/) (2022)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [Learning-based and unrolled motion-compensated reconstruction for cardiac MR CINE imaging](https://mlsanity.com/paper/2209.03671/) (2022)
- [Motion-compensated MR CINE reconstruction with reconstruction-driven motion estimation](https://mlsanity.com/paper/2302.02504/) (2023)
- [Global k-Space Interpolation for Dynamic MRI Reconstruction using Masked Image Modeling](https://mlsanity.com/paper/2307.12672/) (2023)
- [Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI](https://mlsanity.com/paper/2112.09891/) (2021)
- [SelfCoLearn: Self-supervised collaborative learning for accelerating dynamic MR imaging](https://mlsanity.com/paper/2208.03904/) (2022)
- [Deep unfolding as iterative regularization for imaging inverse problems](https://mlsanity.com/paper/2211.13452/) (2022)
- [T2LR-Net: An unrolling network learning transformed tensor low-rank prior for dynamic MR image reconstruction](https://mlsanity.com/paper/2209.03832/) (2022)
- [Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI](https://mlsanity.com/paper/2309.13571/) (2023)
- [Deep Separable Spatiotemporal Learning for Fast Dynamic Cardiac MRI](https://mlsanity.com/paper/2402.15939/) (2024)
- [DP-MDM: Detail-Preserving MR Reconstruction via Multiple Diffusion Models](https://mlsanity.com/paper/2405.05763/) (2024)
- [PISCO: Self-Supervised k-Space Regularization for Improved Neural Implicit k-Space Representations of Dynamic MRI](https://mlsanity.com/paper/2501.09403/) (2025)
- [SRE-CNN: A Spatiotemporal Rotation-Equivariant CNN for Cardiac Cine MR Imaging](https://mlsanity.com/paper/2409.08537/) (2024)
- [Deep unrolling Shrinkage Network for Dynamic MR imaging](https://mlsanity.com/paper/2307.09818/) (2023)
- [MCU-Net: A Multi-prior Collaborative Deep Unfolding Network with Gates-controlled Spatial Attention for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2402.03383/) (2024)
- [K-UNN: k-Space Interpolation With Untrained Neural Network](https://mlsanity.com/paper/2208.05827/) (2022)
- [Dynamic MRI reconstruction using low-rank plus sparse decomposition with smoothness regularization](https://mlsanity.com/paper/2401.16928/) (2024)
- [Attention Incorporated Network for Sharing Low-rank, Image and K-space Information during MR Image Reconstruction to Achieve Single Breath-hold Cardiac Cine Imaging](https://mlsanity.com/paper/2407.03034/) (2024)
- [JotlasNet: Joint Tensor Low-Rank and Attention-based Sparse Unrolling Network for Accelerating Dynamic MRI](https://mlsanity.com/paper/2502.11749/) (2025)
- [A Long Short-term Memory Based Recurrent Neural Network for Interventional MRI Reconstruction](https://mlsanity.com/paper/2203.14769/) (2022)
- [PS-Net: Learned Partially Separable Model for Dynamic MR Imaging](https://mlsanity.com/paper/2205.04073/) (2022)
- [Super-temporal-resolution Photoacoustic Imaging with Dynamic Reconstruction through Implicit Neural Representation in Sparse-view](https://mlsanity.com/paper/2506.03175/) (2025)
- [DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstruction](https://mlsanity.com/paper/2506.10309/) (2025)
- [Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding](https://mlsanity.com/paper/2507.07707/) (2025)

## Abstract (arXiv)

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).