Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction
This work addresses the need for systematic epistemic uncertainty estimation in medical imaging, offering a tool to enhance reliability for radiologists, though it is incremental as it builds on existing variational methods.
The paper tackles the problem of quantifying epistemic uncertainty in deep learning-based MRI reconstruction by introducing a Bayesian variational framework that models regularizer parameters as a learned multivariate Gaussian distribution. The approach yields competitive reconstruction results and provides pixelwise uncertainty estimates that can aid radiologists in assessing reliability.
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.