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End-to-end reconstruction meets data-driven regularization for inverse problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1118-6483
2021 (English)In: Advances in Neural Information Processing Systems, Neural information processing systems foundation , 2021, p. 21413-21425Conference paper, Published paper (Refereed)
Abstract [en]

We propose a new approach for learning end-to-end reconstruction operators based on unpaired training data for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling and essentially seeks to minimize a weighted combination of the expected distortion in the measurement space and the Wasserstein-1 distance between the distributions of the reconstruction and the ground-truth. More specifically, the regularizer in the variational setting is parametrized by a deep neural network and learned simultaneously with the unrolled reconstruction operator. The variational problem is then initialized with the output of the reconstruction network and solved iteratively till convergence. Notably, it takes significantly fewer iterations to converge as compared to variational methods, thanks to the excellent initialization obtained via the unrolled operator. The resulting approach combines the computational efficiency of end-to-end unrolled reconstruction with the well-posedness and noise-stability guarantees of the variational setting. Moreover, we demonstrate with the example of image reconstruction in X-ray computed tomography (CT) that our approach outperforms state-of-the-art unsupervised methods and that it outperforms or is at least on par with state-of-the-art supervised data-driven reconstruction approaches.

Place, publisher, year, edition, pages
Neural information processing systems foundation , 2021. p. 21413-21425
Keywords [en]
Computational efficiency, Computerized tomography, Deep neural networks, Differential equations, Image reconstruction, Iterative methods, Personnel training, Data driven, End to end, ILL-posed inverse problem, Measurement spaces, New approaches, Reconstruction operators, Regularisation, State of the art, Training data, Variational framework, Inverse problems
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-316182ISI: 000922928200004Scopus ID: 2-s2.0-85131577019OAI: oai:DiVA.org:kth-316182DiVA, id: diva2:1699242
Conference
35th Conference on Neural Information Processing Systems, NeurIPS 2021, 6 December - 14 December 2021, Virtual/Online
Note

Part of proceedings: ISBN 978-1-7138-4539-3  

QC 20230921

Available from: 2022-09-27 Created: 2022-09-27 Last updated: 2023-09-21Bibliographically approved

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Mukherjee, SubhadipÖktem, Ozan

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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