Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction

Narnhofer D, Effland A, Kobler E, Hammernik K, Knoll F, Pock T (2022)

Publication Type: Journal article

Publication year: 2022

Journal

IEEE Transactions on Medical Imaging Institute of Electrical and Electronics Engineers (IEEE)

Book Volume: 41

Pages Range: 279-291

Journal Issue: 2

DOI: 10.1109/TMI.2021.3112040

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.

Authors with CRIS profile

Florian Knoll

Involved external institutions

Technische Universität Graz AT Austria (AT) Rheinische Friedrich-Wilhelms-Universität Bonn DE Germany (DE) Johannes Kepler Universität (JKU) Linz AT Austria (AT) Technische Universität München (TUM) DE Germany (DE) New York University (NYU) US United States (USA) (US)

How to cite

APA:

Narnhofer, D., Effland, A., Kobler, E., Hammernik, K., Knoll, F., & Pock, T. (2022). Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction. IEEE Transactions on Medical Imaging, 41(2), 279-291. https://doi.org/10.1109/TMI.2021.3112040

MLA:

Narnhofer, Dominik, et al. "Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction." IEEE Transactions on Medical Imaging 41.2 (2022): 279-291.

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