# Model Learning: Primal Dual Networks for Fast MR imaging

arXiv: https://arxiv.org/abs/1908.02426 · HTML: https://mlsanity.com/paper/1908.02426/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2019.

## Built on by (most cited first, 22 of 22)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [An Optimization-Based Meta-Learning Model for MRI Reconstruction with Diverse Dataset](https://mlsanity.com/paper/2110.00715/) (2021)
- [A Learnable Variational Model for Joint Multimodal MRI Reconstruction and Synthesis](https://mlsanity.com/paper/2204.03804/) (2022)
- [Progressive Divide-and-Conquer via Subsampling Decomposition for Accelerated MRI](https://mlsanity.com/paper/2403.10064/) (2024)
- [An Optimal Control Framework for Joint-channel Parallel MRI Reconstruction without Coil Sensitivities](https://mlsanity.com/paper/2109.09738/) (2021)
- [Deep Unfolding of the DBFB Algorithm with Application to ROI CT Imaging with Limited Angular Density](https://mlsanity.com/paper/2209.13264/) (2022)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing](https://mlsanity.com/paper/2207.13560/) (2022)
- [MRPD: Undersampled MRI reconstruction by prompting a large latent diffusion model](https://mlsanity.com/paper/2402.10609/) (2024)
- [Contrastive Learning for Local and Global Learning MRI Reconstruction](https://mlsanity.com/paper/2111.15200/) (2021)
- [Image Reconstruction for Accelerated MR Scan with Faster Fourier Convolutional Neural Networks](https://mlsanity.com/paper/2306.02886/) (2023)
- [Accelerating Multi-Block Constrained Optimization Through Learning to Optimize](https://mlsanity.com/paper/2409.17320/) (2024)
- [NoSENSE: Learned unrolled cardiac MRI reconstruction without explicit sensitivity maps](https://mlsanity.com/paper/2309.15608/) (2023)
- [DuDoUniNeXt: Dual-domain unified hybrid model for single and multi-contrast undersampled MRI reconstruction](https://mlsanity.com/paper/2403.05256/) (2024)
- [PS-Net: Learned Partially Separable Model for Dynamic MR Imaging](https://mlsanity.com/paper/2205.04073/) (2022)
- [MS-Glance: Bio-Insipred Non-semantic Context Vectors and their Applications in Supervising Image Reconstruction](https://mlsanity.com/paper/2410.23577/) (2024)
- [Zero-shot Dynamic MRI Reconstruction with Global-to-local Diffusion Model](https://mlsanity.com/paper/2411.03723/) (2024)
- [Simultaneous Image Quality Improvement and Artefacts Correction in Accelerated MRI](https://mlsanity.com/paper/2511.23274/) (2025)

## Abstract (arXiv)

Magnetic resonance imaging (MRI) is known to be a slow imaging modality and undersampling in k-space has been used to increase the imaging speed. However, image reconstruction from undersampled k-space data is an ill-posed inverse problem. Iterative algorithms based on compressed sensing have been used to address the issue. In this work, we unroll the iterations of the primal-dual hybrid gradient algorithm to a learnable deep network architecture, and gradually relax the constraints to reconstruct MR images from highly undersampled k-space data. The proposed method combines the theoretical convergence guarantee of optimi-zation methods with the powerful learning capability of deep networks. As the constraints are gradually relaxed, the reconstruction model is finally learned from the training data by updating in k-space and image domain alternatively. Experi-ments on in vivo MR data demonstrate that the proposed method achieves supe-rior MR reconstructions from highly undersampled k-space data over other state-of-the-art image reconstruction methods.