TY - JOUR
T1 - Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction
AU - Narnhofer, Dominik
AU - Effland, Alexander
AU - Kobler, Erich
AU - Hammernik, Kerstin
AU - Knoll, Florian
AU - Pock, Thomas
N1 - Publisher Copyright:
IEEE
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Bayes’ theorem
KW - convolutional neural network
KW - epistemic uncertainty estimation
KW - image reconstruction
KW - magnetic resonance imaging
KW - total deep variation
KW - undersampled MRI
UR - http://www.scopus.com/inward/record.url?scp=85109982458&partnerID=8YFLogxK
U2 - 10.1109/TMI.2021.3112040
DO - 10.1109/TMI.2021.3112040
M3 - Article
AN - SCOPUS:85109982458
SN - 0278-0062
VL - 41
SP - 279
EP - 291
JO - IEEE Transactions on Medical Imaging
JF - IEEE Transactions on Medical Imaging
IS - 2
ER -