# MRI Reconstruction Using Deep Energy-Based Model

arXiv: https://arxiv.org/abs/2109.03237 · HTML: https://mlsanity.com/paper/2109.03237/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 7 Sep 2021.

## Builds on (most cited first, 23 of 23)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Learning Energy-Based Models by Diffusion Recovery Likelihood](https://mlsanity.com/paper/2012.08125/) (2020)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [Residual Energy-Based Models for Text Generation](https://mlsanity.com/paper/2004.11714/) (2020)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss](https://mlsanity.com/paper/1709.00753/) (2017)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Maximum Entropy Generators for Energy-Based Models](https://mlsanity.com/paper/1901.08508/) (2019)
- [A Transfer-Learning Approach for Accelerated MRI using Deep Neural Networks](https://mlsanity.com/paper/1710.02615/) (2017)
- [MR image reconstruction using deep density priors](https://mlsanity.com/paper/1711.11386/) (2017)
- [MRI Reconstruction Using Deep Bayesian Estimation](https://mlsanity.com/paper/1909.01127/) (2019)
- [Lung and Pancreatic Tumor Characterization in the Deep Learning Era: Novel Supervised and Unsupervised Learning Approaches](https://mlsanity.com/paper/1801.03230/) (2018)

## Built on by (most cited first, 8 of 8)

- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction](https://mlsanity.com/paper/2309.00853/) (2023)
- [K-space and Image Domain Collaborative Energy based Model for Parallel MRI Reconstruction](https://mlsanity.com/paper/2203.10776/) (2022)
- [DP-MDM: Detail-Preserving MR Reconstruction via Multiple Diffusion Models](https://mlsanity.com/paper/2405.05763/) (2024)
- [Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstruction](https://mlsanity.com/paper/2411.03758/) (2024)
- [Diffusion-Assisted Frequency Attention Model for Whole-body Low-field MRI Reconstruction](https://mlsanity.com/paper/2507.17764/) (2025)
- [Product-of-Gaussian-Mixture Diffusion Models for Joint Nonlinear MRI Reconstruction](https://mlsanity.com/paper/2605.10629/) (2026)

## Abstract (arXiv)

Purpose: Although recent deep energy-based generative models (EBMs) have shown encouraging results in many image generation tasks, how to take advantage of the self-adversarial cogitation in deep EBMs to boost the performance of Magnetic Resonance Imaging (MRI) reconstruction is still desired. Methods: With the successful application of deep learning in a wide range of MRI reconstruction, a line of emerging research involves formulating an optimization-based reconstruction method in the space of a generative model. Leveraging this, a novel regularization strategy is introduced in this article which takes advantage of self-adversarial cogitation of the deep energy-based model. More precisely, we advocate for alternative learning a more powerful energy-based model with maximum likelihood estimation to obtain the deep energy-based information, represented as image prior. Simultaneously, implicit inference with Langevin dynamics is a unique property of re-construction. In contrast to other generative models for reconstruction, the proposed method utilizes deep energy-based information as the image prior in reconstruction to improve the quality of image. Results: Experiment results that imply the proposed technique can obtain remarkable performance in terms of high reconstruction accuracy that is competitive with state-of-the-art methods, and does not suffer from mode collapse. Conclusion: Algorithmically, an iterative approach was presented to strengthen EBM training with the gradient of energy network. The robustness and the reproducibility of the algorithm were also experimentally validated. More importantly, the proposed reconstruction framework can be generalized for most MRI reconstruction scenarios.