# Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models

arXiv: https://arxiv.org/abs/2606.17343 · HTML: https://mlsanity.com/paper/2606.17343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [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)
- [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)
- [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)
- [A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI](https://mlsanity.com/paper/2303.02586/) (2023)
- [Patch-Based Sparse Representation For Bacterial Detection](https://mlsanity.com/paper/1810.12043/) (2018)
- [Bayesian Uncertainty-Aware MRI Reconstruction](https://mlsanity.com/paper/2603.13439/) (2026)
- [Deconvolution and Restoration of Optical Endomicroscopy Images](https://mlsanity.com/paper/1701.08107/) (2017)

## Abstract (arXiv)

We propose a novel Bayesian framework for joint image reconstruction and uncertainty quantification from compressed sensing magnetic resonance imaging data. The problem is formulated as a linear inverse problem, where prior distributions are assigned to the unknown image parameters. Specifically, the image is assumed to be sparse in a given transform domain. We develop a general framework applicable to any sparsifying transform and demonstrate its performance using (1) a total variation transform based on image spatial gradients and (2) a wavelet-domain transform. Bayesian inference is performed using a split-and-augmented Gibbs sampler, while the resulting non-differentiable conditional distributions are efficiently sampled using a proximal Markov chain Monte Carlo method. The proposed algorithms are validated on both single-coil and multi-coil datasets using various k-space sampling patterns and acceleration factors. The results demonstrate that the proposed Bayesian methods consistently outperform their optimisation-based counterparts in image reconstruction while providing uncertainty estimates for the reconstructed images. Furthermore, the estimated uncertainty maps show a strong correlation with the true reconstruction errors and substantially outperformed deep learning-based uncertainty estimation methods.