NPB-REC: A Non-parametric Bayesian Deep-learning Approach for
  Undersampled MRI Reconstruction with Uncertainty Estimation
Samah Khawaled Moti Freiman
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 \url{https://github.com/samahkh/NPB-REC}.