Title: NPB-REC: Non-parametric Assessment of Uncertainty in Deep-learning-based MRI Reconstruction from Undersampled Data

Abstract: Uncertainty quantification in deep-learning (DL) based image reconstruction models is critical for reliable clinical decision making based on the reconstructed images. We introduce "NPB-REC", a non-parametric fully Bayesian framework for uncertainty assessment in MRI reconstruction from undersampled "k-space" data. We use Stochastic gradient Langevin dynamics (SGLD) during the training phase to characterize the posterior distribution of the network weights. We demonstrated the added-value of our approach on the multi-coil brain MRI dataset, from the fastmri challenge, in comparison to the baseline E2E-VarNet with and without inference-time dropout. Our experiments show that NPB-REC outperforms the baseline by means of reconstruction accuracy (PSNR and SSIM of $34.55$, $0.908$ vs. $33.08$, $0.897$, $p<0.01$) in high acceleration rates ($R=8$). This is also measured in regions of clinical annotations. More significantly, it provides a more accurate estimate of the uncertainty that correlates with the reconstruction error, compared to the Monte-Carlo inference time Dropout method (Pearson correlation coefficient of $R=0.94$ vs. $R=0.91$). The proposed approach has the potential to facilitate safe utilization of DL based methods for MRI reconstruction from undersampled data. Code and trained models are available in \url{this https URL}.