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dc.contributor.authorAspri, A
dc.contributor.authorKorolev, Y
dc.contributor.authorScherzer, O
dc.date.accessioned2022-01-28T14:38:37Z
dc.date.available2022-01-28T14:38:37Z
dc.date.issued2020
dc.date.submitted2020-04-16
dc.identifier.issn0266-5611
dc.identifier.otheripabb61b
dc.identifier.otherabb61b
dc.identifier.otherip-102693.r1
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/333000
dc.description.abstractWe study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can be formulated by using the training data only and without making use of the forward operator. We study convergence and stability of the regularized solutions in view of T. I. Seidman. "Nonconvergence Results for the Application of Least-Squares Estimation to Ill-Posed Problems". Journal of Optimization Theory and Applications 30.4 (1980), pp. 535-547, who showed that regularization by projection is not convergent in general, by giving some insight on the generality of Seidman's nonconvergence example. Moreover, we show, analytically and numerically, that regularization by projection is indeed capable of learning linear operators, such as the Radon transform.
dc.languageen
dc.publisherIOP Publishing
dc.subjectPaper
dc.subjectdata driven regularization
dc.subjectvariational regularization
dc.subjectregularization by projection
dc.subjectinverse problems
dc.subjectGram–Schmidt orthogonalization
dc.titleData driven regularization by projection
dc.typeArticle
dc.date.updated2022-01-28T14:38:36Z
prism.issueIdentifier12
prism.publicationNameInverse Problems
prism.volume36
dc.identifier.doi10.17863/CAM.80424
dcterms.dateAccepted2020-09-08
rioxxterms.versionofrecord10.1088/1361-6420/abb61b
rioxxterms.versionVoR
rioxxterms.licenseref.urihttps://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidKorolev, Y [0000-0002-6339-652X]
dc.contributor.orcidScherzer, O [0000-0001-9378-7452]
dc.identifier.eissn1361-6420
pubs.funder-project-idRoyal Society (NF170045)
pubs.funder-project-idAustrian Science Fund (I3661-N27 SFB F68 F6807-N36)
cam.issuedOnline2020-12-03


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