{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-to-solve-inverse-problems-using","title":"Learning to solve inverse problems using Wasserstein loss","arxiv_id":"1710.10898","date":"2017-10-30","proceeding":null,"authors":["Jonas Adler","Axel Ringh","Ozan Öktem","Johan Karlsson"],"abstract":"We propose using the Wasserstein loss for training in inverse problems. In\nparticular, we consider a learned primal-dual reconstruction scheme for\nill-posed inverse problems using the Wasserstein distance as loss function in\nthe learning. This is motivated by miss-alignments in training data, which when\nusing standard mean squared error loss could severely degrade reconstruction\nquality. We prove that training with the Wasserstein loss gives a\nreconstruction operator that correctly compensates for miss-alignments in\ncertain cases, whereas training with the mean squared error gives a smeared\nreconstruction. Moreover, we demonstrate these effects by training a\nreconstruction algorithm using both mean squared error and optimal transport\nloss for a problem in computerized tomography.","url_abs":"http://arxiv.org/abs/1710.10898v1","url_pdf":"http://arxiv.org/pdf/1710.10898v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-to-solve-inverse-problems-using","repo_url":"https://github.com/odlgroup/odl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MPL-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.10898","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}