Bayesian Uncertainty-Aware MRI Reconstruction

TL;DR

This paper introduces a Bayesian framework for MRI reconstruction that jointly recovers images from under-sampled data and quantifies uncertainty, outperforming traditional compressed sensing methods.

Contribution

It presents a novel Bayesian approach with a Gibbs sampler for MRI reconstruction that integrates uncertainty quantification, a feature lacking in prior methods.

Findings

Outperforms optimization-based compressed sensing algorithms.

Effectively quantifies uncertainty with strong correlation to error maps.

Demonstrates superior performance on single- and multi-coil datasets.

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.