# One-dimensional Deep Low-rank and Sparse Network for Accelerated MRI

arXiv: https://arxiv.org/abs/2112.04721 · HTML: https://mlsanity.com/paper/2112.04721/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 63 references that are in the map.
- First posted on arXiv 9 Dec 2021.

## Builds on (most cited first, 18 of 18)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019)
- [Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)](https://mlsanity.com/paper/1912.03433/) (2019)
- [Accelerated MRI Reconstruction with Separable and Enhanced Low-Rank Hankel Regularization](https://mlsanity.com/paper/2107.11650/) (2021)
- [Image Reconstruction with Low-rankness and Self-consistency of k-space Data in Parallel MRI](https://mlsanity.com/paper/1909.02846/) (2019)
- [A Sparse Model-inspired Deep Thresholding Network for Exponential Signal Reconstruction -- Application in Fast Biological Spectroscopy](https://mlsanity.com/paper/2012.14830/) (2020)
- [Structured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learning](https://mlsanity.com/paper/1910.12162/) (2019)
- [Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction](https://mlsanity.com/paper/1503.02945/) (2015)
- [pISTA-SENSE-ResNet for Parallel MRI Reconstruction](https://mlsanity.com/paper/1910.00650/) (2019)
- [A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery](https://mlsanity.com/paper/1609.07429/) (2016)
- [XCloud-pFISTA: A Medical Intelligence Cloud for Accelerated MRI](https://mlsanity.com/paper/2104.08824/) (2021)
- [A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery](https://mlsanity.com/paper/1811.10778/) (2018)
- [Accelerating MR Imaging via Deep Chambolle-Pock Network](https://mlsanity.com/paper/1905.09525/) (2019)

## Built on by (most cited first, 27 of 27)

- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [On Efficient Training of Large-Scale Deep Learning Models: A Literature Review](https://mlsanity.com/paper/2304.03589/) (2023)
- [One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction](https://mlsanity.com/paper/2307.13220/) (2023)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [A Faithful Deep Sensitivity Estimation for Accelerated Magnetic Resonance Imaging](https://mlsanity.com/paper/2210.12723/) (2022)
- [Deep Separable Spatiotemporal Learning for Fast Dynamic Cardiac MRI](https://mlsanity.com/paper/2402.15939/) (2024)
- [Encoding Enhanced Complex CNN for Accurate and Highly Accelerated MRI](https://mlsanity.com/paper/2306.11977/) (2023)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [Paired Conditional Generative Adversarial Network for Highly Accelerated Liver 4D MRI](https://mlsanity.com/paper/2405.12357/) (2024)
- [Cloud-Magnetic Resonance Imaging System: In the Era of 6G and Artificial Intelligence](https://mlsanity.com/paper/2310.11641/) (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)
- [Enabling Ultra-Fast Cardiovascular Imaging Across Heterogeneous Clinical Environments with A Generalist Foundation Model and Multimodal Database](https://mlsanity.com/paper/2512.21652/) (2025)
- [Adaptive Local Neighborhood-based Neural Networks for MR Image Reconstruction from Undersampled Data](https://mlsanity.com/paper/2206.00775/) (2022)
- [Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2212.05503/) (2022)
- [A Dynamics Theory of Implicit Regularization in Deep Low-Rank Matrix Factorization](https://mlsanity.com/paper/2212.14150/) (2022)
- [AliasNet: Alias Artefact Suppression Network for Accelerated Phase-Encode MRI](https://mlsanity.com/paper/2302.08861/) (2023)
- [Simultaneous Deep Learning of Myocardium Segmentation and T2 Quantification for Acute Myocardial Infarction MRI](https://mlsanity.com/paper/2405.10570/) (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)
- [Physics-informed Deep Diffusion MRI Reconstruction with Synthetic Data: Break Training Data Bottleneck in Artificial Intelligence](https://mlsanity.com/paper/2210.11388/) (2022)
- [Convex Dual Theory Analysis of Two-Layer Convolutional Neural Networks with Soft-Thresholding](https://mlsanity.com/paper/2304.06959/) (2023)
- [A plug-and-play synthetic data deep learning for undersampled magnetic resonance image reconstruction](https://mlsanity.com/paper/2309.06681/) (2023)
- [OneNet: A Channel-Wise 1D Convolutional U-Net](https://mlsanity.com/paper/2411.09838/) (2024)
- [Advancing MRI Reconstruction: A Systematic Review of Deep Learning and Compressed Sensing Integration](https://mlsanity.com/paper/2501.14158/) (2025)
- [ALL-PET: A Low-resource and Low-shot PET Foundation Model in Projection Domain](https://mlsanity.com/paper/2509.09130/) (2025)
- [Robust High-Resolution Multi-Organ Diffusion MRI Using Synthetic-Data-Tuned Prompt Learning](https://mlsanity.com/paper/2510.15400/) (2025)
- [Analyse comparative d'algorithmes de restauration en architecture d'epli'ee pour des signaux chromatographiques parcimonieux](https://mlsanity.com/paper/2510.18760/) (2025)
- [CLEAR: Complex Learned Explicit Analytical Regularization for Ultra-Accelerated 4D Flow CMR Reconstruction](https://mlsanity.com/paper/2609.22950/) (2026)

## Abstract (arXiv)

Deep learning has shown astonishing performance in accelerated magnetic resonance imaging (MRI). Most state-of-the-art deep learning reconstructions adopt the powerful convolutional neural network and perform 2D convolution since many magnetic resonance images or their corresponding k-space are in 2D. In this work, we present a new approach that explores the 1D convolution, making the deep network much easier to be trained and generalized. We further integrate the 1D convolution into the proposed deep network, named as One-dimensional Deep Low-rank and Sparse network (ODLS), which unrolls the iteration procedure of a low-rank and sparse reconstruction model. Extensive results on in vivo knee and brain datasets demonstrate that, the proposed ODLS is very suitable for the case of limited training subjects and provides improved reconstruction performance than state-of-the-art methods both visually and quantitatively. Additionally, ODLS also shows nice robustness to different undersampling scenarios and some mismatches between the training and test data. In summary, our work demonstrates that the 1D deep learning scheme is memory-efficient and robust in fast MRI.