Bayesian Uncertainty-Aware MRI Reconstruction

2026-03-13

AI Summary

This work addresses the problem of magnetic resonance image reconstruction and uncertainty quantification from undersampled k-space data by formulating reconstruction as a Bayesian linear inverse problem. A total variation prior is introduced to capture the sparsity of image gradients, and an efficient split-augmented Gibbs sampler is designed for posterior inference. The proposed method achieves, for the first time in MRI reconstruction, simultaneous high-fidelity imaging and pixel-wise uncertainty estimation, with the quantified uncertainties showing strong correlation with actual reconstruction errors. Experiments on both single-coil and multi-coil datasets demonstrate that the approach outperforms conventional compressed sensing algorithms in reconstruction quality while providing reliable and interpretable uncertainty measures.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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.

Problem

• MRI reconstruction
• uncertainty quantification
• Bayesian inference
• under-sampled k-space
• inverse problem

Innovation

• Bayesian MRI reconstruction
• uncertainty quantification
• total variation prior
• Markov chain Monte Carlo
• compressed sensing