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Learning to solve i...
Learning to solve inverse problems using Wasserstein loss
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- Adler, Jonas (author)
- KTH,Matematik (Avd.),Elekta, Box 7593, 103 93 Stockholm, Sweden
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- Ringh, Axel (author)
- KTH,Optimeringslära och systemteori
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- Öktem, Ozan (author)
- KTH,Matematik (Avd.)
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- Karlsson, Johan (author)
- KTH,Optimeringslära och systemteori
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KTH Matematik (Avd) (creator_code:org_t)
- English.
- Related links:
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https://urn.kb.se/re...
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Abstract
Subject headings
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- We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Medicinteknik -- Medicinsk bildbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Medical Engineering -- Medical Image Processing (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- Mathematics
- Matematik
- Tillämpad matematik och beräkningsmatematik
- Applied and Computational Mathematics
Publication and Content Type
- vet (subject category)
- ovr (subject category)
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