# Learned Half-Quadratic Splitting Network for MR Image Reconstruction

arXiv: https://arxiv.org/abs/2112.09760 · HTML: https://mlsanity.com/paper/2112.09760/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 17 Dec 2021.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [OCMR (v1.0)--Open-Access Multi-Coil k-Space Dataset for Cardiovascular Magnetic Resonance Imaging](https://mlsanity.com/paper/2008.03410/) (2020)
- [Deep learning for fast MR imaging: a review for learning reconstruction from incomplete k-space data](https://mlsanity.com/paper/2012.08931/) (2020)
- [An Adaptive Intelligence Algorithm for Undersampled Knee MRI Reconstruction](https://mlsanity.com/paper/2004.07339/) (2020)
- [Memory-efficient Learning for Large-scale Computational Imaging -- NeurIPS deep inverse workshop](https://mlsanity.com/paper/1912.05098/) (2019)
- [Simulating single-coil MRI from the responses of multiple coils](https://mlsanity.com/paper/1811.08026/) (2018)

## Built on by (most cited first, 5 of 5)

- [GA-HQS: MRI reconstruction via a generically accelerated unfolding approach](https://mlsanity.com/paper/2304.02883/) (2023)
- [Enhancing Electrical Impedance Tomography reconstruction using Learned Half-Quadratic Splitting Networks with Anderson Acceleration](https://mlsanity.com/paper/2304.14491/) (2023)
- [Joint Edge Optimization Deep Unfolding Network for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2405.05564/) (2024)
- [Re-Visible Dual-Domain Self-Supervised Deep Unfolding Network for MRI Reconstruction](https://mlsanity.com/paper/2501.03737/) (2025)
- [Majorization-Minimization Networks for Inverse Problems: An Application to EEG Imaging](https://mlsanity.com/paper/2602.03855/) (2026)

## Abstract (arXiv)

Magnetic Resonance (MR) image reconstruction from highly undersampled k-space data is critical in accelerated MR imaging (MRI) techniques. In recent years, deep learning-based methods have shown great potential in this task. This paper proposes a learned half-quadratic splitting algorithm for MR image reconstruction and implements the algorithm in an unrolled deep learning network architecture. We compare the performance of our proposed method on a public cardiac MR dataset against DC-CNN and LPDNet, and our method outperforms other methods in both quantitative results and qualitative results with fewer model parameters and faster reconstruction speed. Finally, we enlarge our model to achieve superior reconstruction quality, and the improvement is 1.76 dB and 2.74 dB over LPDNet in peak signal-to-noise ratio on 5× and 10× acceleration, respectively. Code for our method is publicly available at https://github.com/hellopipu/HQS-Net.