Multiparameter Uncertainty Mapping in Quantitative Molecular MRI using a Physics-Structured Variational Autoencoder (PS-VAE)

Parallel imaging techniques reduce magnetic resonance imaging (MRI) scan time but image quality degrades as the acceleration factor increases. In clinical practice, conservative acceleration factors are chosen because no mechanism exists to automatically assess the diagnostic quality of undersampled reconstructions. This work introduces a general framework for pixel-wise uncertainty quantification in parallel MRI reconstructions, enabling automatic identification of unreliable regions without access to any ground-truth reference image. Our method integrates conformal quantile regression with image reconstruction methods to estimate statistically rigorous pixel-wise uncertainty intervals. We trained and evaluated our model on Cartesian undersampled brain and knee data obtained from the fastMRI dataset using acceleration factors ranging from 2 to 10. An end-to-end Variational Network was used for image reconstruction. Quantitative experiments demonstrate strong agreement between predicted uncertainty maps and true reconstruction error. Using our method, the corresponding Pearson correlation coefficient was higher than 90% at acceleration levels at and above four-fold; whereas it dropped to less than 70% when the uncertainty was computed using a simpler a heuristic notion (magnitude of the residual). Qualitative examples further show the uncertainty maps based on quantile regression capture the magnitude and spatial distribution of reconstruction errors across acceleration factors, with regions of elevated uncertainty aligning with pathologies and artifacts. The proposed framework enables evaluation of reconstruction quality without access to fully-sampled ground-truth reference images. It represents a step toward adaptive MRI acquisition protocols that may be able to dynamically balance scan time and diagnostic reliability.

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.

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.