Adversarial Regularizers in Inverse Problems. Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying data-driven approaches to inverse problems, using a neural network as a regularization functional. The network learns to discriminate between the distribution of ground truth images and the distribution of unregularized reconstructions. Once trained, the network is applied to the inverse problem by solving the corresponding variational problem. Unlike other data-based approaches for inverse problems, the algorithm can be applied even if only unsupervised training data is available. Experiments demonstrate the potential of the framework for denoising on the BSDS dataset and for computed tomography reconstruction on the LIDC dataset.

References in zbMATH (referenced in 16 articles )

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  1. Gupta, Rachit; Jaiman, Rajeev: A hybrid partitioned deep learning methodology for moving interface and fluid-structure interaction (2022)
  2. Habring, Andreas; Holler, Martin: A generative variational model for inverse problems in imaging (2022)
  3. Heaton, Howard; Fung, Samy Wu; Lin, Alex Tong; Osher, Stanley; Yin, Wotao: Wasserstein-based projections with applications to inverse problems (2022)
  4. Arridge, Simon R. (ed.); Maaß, Peter (ed.); Schönlieb, Carola-Bibiane (ed.): Deep learning for inverse problems. Abstracts from the workshop held March 7--13, 2021 (hybrid meeting) (2021)
  5. Bubba, Tatiana A.; Galinier, Mathilde; Lassas, Matti; Prato, Marco; Ratti, Luca; Siltanen, Samuli: Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography (2021)
  6. Celledoni, Elena; Ehrhardt, Matthias J.; Etmann, Christian; Owren, Brynjulf; Schönlieb, Carola-Bibiane; Sherry, Ferdia: Equivariant neural networks for inverse problems (2021)
  7. de Hoop, Maarten V.; Lassas, Matti; Wong, Christopher A.: Deep learning architectures for nonlinear operator functions and nonlinear inverse problems (2021)
  8. Heaton, Howard; Wu Fung, Samy; Gibali, Aviv; Yin, Wotao: Feasibility-based fixed point networks (2021)
  9. Lunz, Sebastian; Hauptmann, Andreas; Tarvainen, Tanja; Schönlieb, Carola-Bibiane; Arridge, Simon: On learned operator correction in inverse problems (2021)
  10. Obmann, Daniel; Schwab, Johannes; Haltmeier, Markus: Deep synthesis network for regularizing inverse problems (2021)
  11. Pinetz, Thomas; Kobler, Erich; Pock, Thomas; Effland, Alexander: Shared prior learning of energy-based models for image reconstruction (2021)
  12. Agnelli, J. P.; Çöl, A.; Lassas, Matti; Murthy, Rashmi; Santacesaria, Matteo; Siltanen, Samuli: Classification of stroke using neural networks in electrical impedance tomography (2020)
  13. Aspri, Andrea; Korolev, Yury; Scherzer, Otmar: Data driven regularization by projection (2020)
  14. Baguer, Daniel Otero; Leuschner, Johannes; Schmidt, Maximilian: Computed tomography reconstruction using deep image prior and learned reconstruction methods (2020)
  15. Chambolle, A.; Holler, M.; Pock, T.: A convex variational model for learning convolutional image atoms from incomplete data (2020)
  16. Arridge, Simon; Maass, Peter; Öktem, Ozan; Schönlieb, Carola-Bibiane: Solving inverse problems using data-driven models (2019)