Predictive uncertainty in deep learning-based MR image reconstruction using deep ensembles: Evaluation on the fastMRI data set

Purpose: To estimate pixel-wise predictive uncertainty for deep learning-based MR image reconstruction and to examine the impact of domain shifts and architecture robustness. Methods: Uncertainty prediction could provide a measure for robustness of deep learning (DL)-based MR image reconstruction from undersampled data. DL methods bear the risk of inducing reconstruction errors like in-painting of unrealistic structures or missing pathologies. These errors may be obscured by visual realism of DL reconstruction and thus remain undiscovered. Furthermore, most methods are task-agnostic and not well calibrated to domain shifts. We propose a strategy that estimates aleatoric (data) and epistemic (model) uncertainty, which entails training a deep ensemble (epistemic) with nonnegative log-likelihood (aleatoric) loss in addition to the conventional applied losses terms. The proposed procedure can be paired with any DL reconstruction, enabling investigations of their predictive uncertainties on a pixel level. Five different architectures were investigated on the fastMRI database. The impact on the examined uncertainty of in-distributional and out-of-distributional data with changes to undersampling pattern, imaging contrast, imaging orientation, anatomy, and pathology were explored. Results: Predictive uncertainty could be captured and showed good correlation to normalized mean squared error. Uncertainty was primarily focused along the aliased anatomies and on hyperintense and hypointense regions. The proposed uncertainty measure was able to detect disease prevalence shifts. Distinct predictive uncertainty patterns were observed for changing network architectures. Conclusion: The proposed approach enables aleatoric and epistemic uncertainty prediction for DL-based MR reconstruction with an interpretable examination on a pixel level.