Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction

TL;DR

This paper introduces a Bayesian variational framework for MRI reconstruction that quantifies epistemic uncertainty, providing both improved reconstruction and a reliable uncertainty measure to assist radiologists.

Contribution

It presents a novel Bayesian variational method to estimate epistemic uncertainty in deep learning-based MRI reconstruction, combining a learned regularizer with stochastic parameter sampling.

Findings

Competitive MRI reconstruction results

Accurate pixelwise epistemic uncertainty quantification

Enhanced visualization of reconstruction reliability

Abstract

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.