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Task adapted recons...
Task adapted reconstruction for inverse problems
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- Adler, Jonas (författare)
- KTH,Matematik (Avd.),DeepMind, 6 Pancras Square, London, N1C 4AG, United Kingdom,KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden.;DeepMind, 6 Pancras Sq, London N1C 4AG, England.
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- Lunz, Sebastian (författare)
- Univ Cambridge, Ctr Math Sci, Cambridge CB3 0WA, England.
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- Verdier, Olivier (författare)
- KTH,Matematik (Avd.),Department of Computing, Mathematics and Physics, Western Norway University of Applied Sciences, Bergen, Norway,KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden.;Western Norway Univ Appl Sci, Dept Comp Math & Phys, Bergen, Norway.
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- Schonlieb, Carola-Bibiane (författare)
- Univ Cambridge, Ctr Math Sci, Cambridge CB3 0WA, England.
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- Öktem, Ozan, 1969- (författare)
- Uppsala universitet,KTH,Matematik (Avd.),Division of Scientific Computing, Department of Information Technology, Uppsala University,Avdelningen för beräkningsvetenskap,KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
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KTH Matematik (Avd) (creator_code:org_t)
- 2022-05-31
- 2022
- Engelska.
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 38:7
- Relaterad länk:
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https://doi.org/10.1...
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http://arxiv.org/pdf...
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https://uu.diva-port... (primary) (Raw object)
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https://urn.kb.se/re...
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https://doi.org/10.1...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- The paper considers the problem of performing a post-processing task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and post-processing as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the post-processing task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any post-processing that can be encoded as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation.
Ämnesord
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- inverse problems
- image reconstruction
- tomography
- deep learning
- feature reconstruction
- segmentation
- classification
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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