We propose an extended family of structured spatial priors that incorporates the total variation (TV) function with ℓp norms. The prior is proven to be proper and incorporated into a Bayesian regression framework to enable uncertainty quantification in T1 mapping, with posterior inference performed using the No-U-Turn Sampler (NUTS). This TV--ℓp construction is proven to constitute a well-defined family of prior distributions, and it naturally enforces spatial consistency and smooth variations in the estimated parameter maps. The method was evaluated in comparison to maximum-likelihood estimation and several Bayesian alternative priors based on the uniform, Gamma, and bounded TV priors. The evaluation includes experiments on synthetic brain and cardiac T1 mapping datasets, as well as a real in-vivo breast T1 mapping dataset. The results show that the TV--ℓp prior yields more concentrated posterior densities, indicating reduced uncertainty. It also consistently achieves lower variance and smaller (negative) bias, leading to more reliable estimates. Overall, embedding a TV-based structured penalty along with ℓp norms in a prior in a Bayesian model improves spatial coherence in T1 maps and enhances uncertainty quantification, offering a robust approach for T1 mapping with uncertainties.
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.
Ahmed Karam Eldaly, Matteo Figini, Daniel C. Alexander
Quantitative T2* maps have strong potential for biomarker discovery but are limited by long scan times, rendering them impractical in clinical settings. Significant acceleration can be achieved through undersampling in k-space combined with learning-based reconstruction. However, reconstruction artifacts and noise can propagate into downstream T2* fitting, degrading its accuracy. We introduce CUPA-T2*, a framework that explicitly propagates voxel-wise inter-echo uncertainty from stochastic Monte Carlo dropout reconstructions to downstream T2* fitting via covariance-aware sampling. T2* fitting is performed with a heteroscedastic MLP and a correlation-based regularizer that encourages alignment between predicted variance and reconstruction uncertainty. Experiments on accelerated brain MRI data show tissue-dependent behavior: CUPA-T2* achieves competitive overall T2* fitting performance and improves white-matter performance at higher accelerations. Compared with a heteroscedastic baseline, the proposed framework substantially increases alignment between reconstruction uncertainty and predicted T2* variance, while also revealing a trade-off with calibration (ECE) and selective prediction performance (AURC). CUPA-T2* enables reconstruction uncertainty-aware T2* fitting and delivers voxel-wise uncertainty maps to support the interpretation of quantitative T2* estimates.
Gideon N. L. Rouwendaal, Natascha Niessen, Hannah Eichhorn +3
MRI provides excellent soft-tissue contrast without ionizing radiation, but long acquisition times increase patient discomfort while also raising exam costs and limiting scanner throughput. A common approach to reduce scan time is to acquire fewer measurements, which yields an ill-posed linear inverse problem; recovering diagnostic-quality images therefore requires incorporating prior knowledge beyond the measured data. In follow-up exams, the most recent prior scan of a patient can provide a highly informative subject-specific context, but practical use is complicated by temporal changes (including pathology progression), misalignment between scans, and protocol drift across acquisitions. In this work, we introduce L-TGVN, a Longitudinal Trust-Guided Variational Network that leverages prior scans as side information to reconstruct the current scan from heavily undersampled measurements. Crucially, L-TGVN constrains the influence of prior scans to be consistent with the acquired measurements. Unlike many existing longitudinal reconstruction methods, it does not require explicit pre-registration between prior and current scans. It further accommodates differences in acquisition protocols across visits (e.g., changes in sequence parameters). We evaluate L-TGVN against matched-capacity baselines, including prior-guided methods and methods that do not use longitudinal priors, and observe consistent improvements in standard quantitative metrics together with better preservation of fine structures at challenging accelerations. Source code is available at github.com/sodicksonlab/L-TGVN.