Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models

• URL: http://arxiv.org/abs/2606.17343v2
• Date: Sun, 21 Jun 2026 11:17:19 GMT
• Title: Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models
• Abstract summary: We propose a novel framework for joint image reconstruction and uncertainty quantification from compressed sensing magnetic resonance imaging data.<n>The problem is formulated as a linear inverse problem, where prior distributions are assigned to the unknown image parameters.<n>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.
• Score: 5.452868777437004
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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