Bayesian Uncertainty-Aware MRI Reconstruction
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915861636317184 |
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| author | Eldaly, Ahmed Karam Figini, Matteo Alexander, Daniel C. |
| author_facet | Eldaly, Ahmed Karam Figini, Matteo Alexander, Daniel C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13439 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian Uncertainty-Aware MRI Reconstruction Eldaly, Ahmed Karam Figini, Matteo Alexander, Daniel C. Image and Video Processing Computer Vision and Pattern Recognition 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. |
| title | Bayesian Uncertainty-Aware MRI Reconstruction |
| topic | Image and Video Processing Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2603.13439 |