Bayesian Uncertainty-Aware MRI Reconstruction
This work addresses uncertainty quantification in MRI reconstruction for medical imaging applications, but it is incremental as it builds on Bayesian methods with a total variation prior.
The authors tackled the problem of reconstructing MRI images from under-sampled k-space measurements while quantifying uncertainty, achieving superior performance over compressed sensing algorithms and showing strong correlation between uncertainty and error maps.
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.