# Bayesian Uncertainty-Aware MRI Reconstruction

arXiv: https://arxiv.org/abs/2603.13439 · HTML: https://mlsanity.com/paper/2603.13439/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 13 Mar 2026.

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

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [Split-and-augmented Gibbs sampler - Application to large-scale inference problems](https://mlsanity.com/paper/1804.05809/) (2018)
- [Multi-Coil MRI Reconstruction Challenge -- Assessing Brain MRI Reconstruction Models and their Generalizability to Varying Coil Configurations](https://mlsanity.com/paper/2011.07952/) (2020)
- [Image Reconstruction with Low-rankness and Self-consistency of k-space Data in Parallel MRI](https://mlsanity.com/paper/1909.02846/) (2019)
- [OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI](https://mlsanity.com/paper/1805.00524/) (2018)
- [The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution](https://mlsanity.com/paper/2206.13894/) (2022)
- [A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI](https://mlsanity.com/paper/2303.02586/) (2023)

## Built on by (most cited first, 3 of 3)

- [Low-Field Magnetic Resonance Image Quality Enhancement using Undersampled k-Space and Out-of-Distribution Generalisation](https://mlsanity.com/paper/2603.14120/) (2026)
- [Low-Field Magnetic Resonance Image Enhancement using Undersampled k-Space](https://mlsanity.com/paper/2603.14125/) (2026)
- [Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models](https://mlsanity.com/paper/2606.17343/) (2026)

## Abstract (arXiv)

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior distributions are assigned to the unknown model parameters. Specifically, we assume the target image is sparse in its spatial gradient and impose a total variation prior model. A Markov chain Monte Carlo (MCMC) method, based on a split-and-augmented Gibbs sampler, is then used to sample from the resulting joint posterior distribution of the unknown parameters. Experiments conducted using single- and multi-coil datasets demonstrate the superior performance of the proposed framework over optimisation-based compressed sensing algorithms. Additionally, our framework effectively quantifies uncertainty, showing strong correlation with error maps computed from reconstructed and ground-truth images.