NPB-REC: A non-parametric Bayesian deep-learning approach for undersampled MRI reconstruction with uncertainty estimation.

The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the lack of verified methods to quantify the uncertainty in the reconstructed images hampered clinical applicability. We introduce "NPB-REC", a non-parametric fully Bayesian framework, for MRI reconstruction from undersampled data with uncertainty estimation. We use Stochastic Gradient Langevin Dynamics during training to characterize the posterior distribution of the network parameters. This enables us to both improve the quality of the reconstructed images and quantify the uncertainty in the reconstructed images. We demonstrate the efficacy of our approach on a multi-coil MRI dataset from the fastMRI challenge and compare it to the baseline End-to-End Variational Network (E2E-VarNet). Our approach outperforms the baseline in terms of reconstruction accuracy by means of PSNR and SSIM (34.55, 0.908 vs. 33.08, 0.897, p<0.01, acceleration rate R=8) and provides uncertainty measures that correlate better with the reconstruction error (Pearson correlation, R=0.94 vs. R=0.91). Additionally, our approach exhibits better generalization capabilities against anatomical distribution shifts (PSNR and SSIM of 32.38, 0.849 vs. 31.63, 0.836, p<0.01, training on brain data, inference on knee data, acceleration rate R=8). NPB-REC has the potential to facilitate the safe utilization of deep learning-based methods for MRI reconstruction from undersampled data. Code and trained models are available at https://github.com/samahkh/NPB-REC.

NPBDREG: Uncertainty assessment in diffeomorphic brain MRI registration using a non-parametric Bayesian deep-learning based approach.

Quantification of uncertainty in deep-neural-networks (DNN) based image registration algorithms plays a critical role in the deployment of image registration algorithms for clinical applications such as surgical planning, intraoperative guidance, and longitudinal monitoring of disease progression or treatment efficacy as well as in research-oriented processing pipelines. Currently available approaches for uncertainty estimation in DNN-based image registration algorithms may result in sub-optimal clinical decision making due to potentially inaccurate estimation of the uncertainty of the registration stems for the assumed parametric distribution of the registration latent space. We introduce NPBDREG, a fully non-parametric Bayesian framework for uncertainty estimation in DNN-based deformable image registration by combining an Adam optimizer with stochastic gradient Langevin dynamics (SGLD) to characterize the underlying posterior distribution through posterior sampling. Thus, it has the potential to provide uncertainty estimates that are highly correlated with the presence of out of distribution data. We demonstrated the added-value of NPBDREG, compared to the baseline probabilistic VoxelMorph model (PrVXM), on brain MRI image registration using 390 image pairs from four publicly available databases: MGH10, CMUC12, ISBR18 and LPBA40. The NPBDREG shows a better correlation of the predicted uncertainty with out-of-distribution data (r > 0.95 vs. r < 0.5) as well as a ~ 7.3 % improvement in the registration accuracy (Dice score, 0.74 vs. 0.69, p â‰ª 0.01), and a ~ 18 % improvement in registration smoothness (percentage of folds in the deformation field, 0.014 vs. 0.017, p â‰ª 0.01). Finally, NPBDREG demonstrated a better generalization capability for data corrupted by a mixed structure noise (Dice score of 0.73 vs. 0.69, p â‰ª 0.01) compared to the baseline PrVXM approach.