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Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction

2021; Institute of Electrical and Electronics Engineers; Volume: 41; Issue: 2 Linguagem: Inglês

10.1109/tmi.2021.3112040

1558-254X

Dominik Narnhofer, Alexander Effland, Erich Kobler, Kerstin Hammernik, Florian Knöll, Thomas Pock,

Radiomics and Machine Learning in Medical Imaging

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.