# Uncertainty Quantification in Deep MRI Reconstruction

arXiv: https://arxiv.org/abs/1901.11228 · HTML: https://mlsanity.com/paper/1901.11228/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2019.

## Built on by (most cited first, 30 of 49)

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [A Review of Uncertainty Estimation and its Application in Medical Imaging](https://mlsanity.com/paper/2302.08119/) (2023)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [Global-Local Transformer for Brain Age Estimation](https://mlsanity.com/paper/2109.01663/) (2021)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)
- [UnCRtainTS: Uncertainty Quantification for Cloud Removal in Optical Satellite Time Series](https://mlsanity.com/paper/2304.05464/) (2023)
- [SMRD: SURE-based Robust MRI Reconstruction with Diffusion Models](https://mlsanity.com/paper/2310.01799/) (2023)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging](https://mlsanity.com/paper/2306.01630/) (2023)
- [A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problems](https://mlsanity.com/paper/2210.13389/) (2022)
- [A Survey of Emerging Applications of Diffusion Probabilistic Models in MRI](https://mlsanity.com/paper/2311.11383/) (2023)
- [An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression](https://mlsanity.com/paper/2504.18433/) (2025)
- [Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction](https://mlsanity.com/paper/2405.18527/) (2024)
- [High Fidelity Deep Learning-based MRI Reconstruction with Instance-wise Discriminative Feature Matching Loss](https://mlsanity.com/paper/2108.12460/) (2021)
- [An Uncertainty-aware Loss Function for Training Neural Networks with Calibrated Predictions](https://mlsanity.com/paper/2110.03260/) (2021)
- [BayTTA: Uncertainty-aware medical image classification with optimized test-time augmentation using Bayesian model averaging](https://mlsanity.com/paper/2406.17640/) (2024)
- [Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging](https://mlsanity.com/paper/2504.07696/) (2025)
- [NPB-REC: A Non-parametric Bayesian Deep-learning Approach for Undersampled MRI Reconstruction with Uncertainty Estimation](https://mlsanity.com/paper/2404.04550/) (2024)
- [Posterior temperature optimized Bayesian models for inverse problems in medical imaging](https://mlsanity.com/paper/2202.00986/) (2022)
- [PixCUE: Joint Uncertainty Estimation and Image Reconstruction in MRI using Deep Pixel Classification](https://mlsanity.com/paper/2303.00111/) (2023)
- [Metric-Guided Conformal Bounds for Probabilistic Image Reconstruction](https://mlsanity.com/paper/2404.15274/) (2024)
- [Uncertainty Quantification for Clinical Outcome Predictions with (Large) Language Models](https://mlsanity.com/paper/2411.03497/) (2024)
- [Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery](https://mlsanity.com/paper/2206.05049/) (2022)
- [Achieving Well-Informed Decision-Making in Drug Discovery: A Comprehensive Calibration Study using Neural Network-Based Structure-Activity Models](https://mlsanity.com/paper/2407.14185/) (2024)
- [pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularization](https://mlsanity.com/paper/2411.00605/) (2024)

## Abstract (arXiv)

Reliable MRI is crucial for accurate interpretation in therapeutic and diagnostic tasks. However, undersampling during MRI acquisition as well as the overparameterized and non-transparent nature of deep learning (DL) leaves substantial uncertainty about the accuracy of DL reconstruction. With this in mind, this study aims to quantify the uncertainty in image recovery with DL models. To this end, we first leverage variational autoencoders (VAEs) to develop a probabilistic reconstruction scheme that maps out (low-quality) short scans with aliasing artifacts to the diagnostic-quality ones. The VAE encodes the acquisition uncertainty in a latent code and naturally offers a posterior of the image from which one can generate pixel variance maps using Monte-Carlo sampling. Accurately predicting risk requires knowledge of the bias as well, for which we leverage Stein's Unbiased Risk Estimator (SURE) as a proxy for mean-squared-error (MSE). Extensive empirical experiments are performed for Knee MRI reconstruction under different training losses (adversarial and pixel-wise) and unrolled recurrent network architectures. Our key observations indicate that: 1) adversarial losses introduce more uncertainty; and 2) recurrent unrolled nets reduce the prediction uncertainty and risk.