# NPB-REC: A Non-parametric Bayesian Deep-learning Approach for Undersampled MRI Reconstruction with Uncertainty Estimation

arXiv: https://arxiv.org/abs/2404.04550 · HTML: https://mlsanity.com/paper/2404.04550/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 6 Apr 2024.

## Builds on (most cited first, 29 of 29)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss](https://mlsanity.com/paper/1709.00753/) (2017)
- [GANs for Medical Image Analysis](https://mlsanity.com/paper/1809.06222/) (2018)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [Uncertainty Quantification in Deep MRI Reconstruction](https://mlsanity.com/paper/1901.11228/) (2019)
- [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019)
- [MR image reconstruction using deep density priors](https://mlsanity.com/paper/1711.11386/) (2017)
- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)
- [MRI Reconstruction Using Deep Bayesian Estimation](https://mlsanity.com/paper/1909.01127/) (2019)
- [fastMRI+: Clinical Pathology Annotations for Knee and Brain Fully Sampled Multi-Coil MRI Data](https://mlsanity.com/paper/2109.03812/) (2021)
- [Uncertainty-Guided Mutual Consistency Learning for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2112.02508/) (2021)
- [Multi-Stage Variational Auto-Encoders for Coarse-to-Fine Image Generation](https://mlsanity.com/paper/1705.07202/) (2017)
- [i-RIM applied to the fastMRI challenge](https://mlsanity.com/paper/1910.08952/) (2019)
- [Fine-tuning deep learning model parameters for improved super-resolution of dynamic MRI with prior-knowledge](https://mlsanity.com/paper/2102.02711/) (2021)
- [Adversarial Robustness of MR Image Reconstruction under Realistic Perturbations](https://mlsanity.com/paper/2208.03161/) (2022)
- [Learning to Predict Error for MRI Reconstruction](https://mlsanity.com/paper/2002.05582/) (2020)
- [Uncertainty-Aware Temporal Self-Learning (UATS): Semi-Supervised Learning for Segmentation of Prostate Zones and Beyond](https://mlsanity.com/paper/2104.03840/) (2021)
- [NPBDREG: Uncertainty Assessment in Diffeomorphic Brain MRI Registration using a Non-parametric Bayesian Deep-Learning Based Approach](https://mlsanity.com/paper/2108.06771/) (2021)

## Built on by (most cited first, 4 of 4)

- [The challenge of uncertainty quantification of large language models in medicine](https://mlsanity.com/paper/2504.05278/) (2025)
- [Advancing MRI Reconstruction: A Systematic Review of Deep Learning and Compressed Sensing Integration](https://mlsanity.com/paper/2501.14158/) (2025)
- [HierarchicalDAEW: Domain-Aware Edge-Weighted Graph Convolution with Evidential Uncertainty for Multi-Section Spatial Gene Expression Prediction from H&E Histology](https://mlsanity.com/paper/2607.20896/) (2026)
- [Evaluating the Safety of Deep Learning-Based Brain MRI Reconstruction](https://mlsanity.com/paper/2608.28714/) (2026)

## Abstract (arXiv)

The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the lack of verified methods to quantify the uncertainty in the reconstructed images hampered clinical applicability. We introduce "NPB-REC", a non-parametric fully Bayesian framework, for MRI reconstruction from undersampled data with uncertainty estimation. We use Stochastic Gradient Langevin Dynamics during training to characterize the posterior distribution of the network parameters. This enables us to both improve the quality of the reconstructed images and quantify the uncertainty in the reconstructed images. We demonstrate the efficacy of our approach on a multi-coil MRI dataset from the fastMRI challenge and compare it to the baseline End-to-End Variational Network (E2E-VarNet). Our approach outperforms the baseline in terms of reconstruction accuracy by means of PSNR and SSIM (34.55, 0.908 vs. 33.08, 0.897, p<0.01, acceleration rate R=8) and provides uncertainty measures that correlate better with the reconstruction error (Pearson correlation, R=0.94 vs. R=0.91). Additionally, our approach exhibits better generalization capabilities against anatomical distribution shifts (PSNR and SSIM of 32.38, 0.849 vs. 31.63, 0.836, p<0.01, training on brain data, inference on knee data, acceleration rate R=8). NPB-REC has the potential to facilitate the safe utilization of deep learning-based methods for MRI reconstruction from undersampled data. Code and trained models are available at urlhttps://github.com/samahkh/NPB-REC.