A study of the one dimensional total generalised variation regularisation problem

Handle URI:
http://hdl.handle.net/10754/597417
Title:
A study of the one dimensional total generalised variation regularisation problem
Authors:
Papafitsoros, Konstantinos; Bredies, Kristian
Abstract:
© 2015 American Institute of Mathematical Sciences. In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with L2 data fitting term. We examine the properties of this model and we calculate exact solutions using simple piecewise affine functions as data terms. We investigate how these solutions behave with respect to the TGV parameters and we verify our results using numerical experiments.
Citation:
Papafitsoros K, Bredies K (2015) A study of the one dimensional total generalised variation regularisation problem. IPI 9: 511–550. Available: http://dx.doi.org/10.3934/ipi.2015.9.511.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Inverse Problems and Imaging
KAUST Grant Number:
KUK-I1007-43
Issue Date:
Mar-2015
DOI:
10.3934/ipi.2015.9.511
Type:
Article
ISSN:
1930-8337
Sponsors:
The first author was supported by UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis, the financial support provided by the EPSRC first grant Nr. EP/J009539/1 ''Sparse & Higher-order Image Restoration" and the Award No. KUK-I1007-43, made by King Abdullah University of Science and Technology (KAUST). The second author is supported by the Austrian Science Fund (FWF) under grant SFB32 (SFB ''Mathematical Optimization and Applications in the Biomedical Sciences").
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Full metadata record

DC FieldValue Language
dc.contributor.authorPapafitsoros, Konstantinosen
dc.contributor.authorBredies, Kristianen
dc.date.accessioned2016-02-25T12:32:49Zen
dc.date.available2016-02-25T12:32:49Zen
dc.date.issued2015-03en
dc.identifier.citationPapafitsoros K, Bredies K (2015) A study of the one dimensional total generalised variation regularisation problem. IPI 9: 511–550. Available: http://dx.doi.org/10.3934/ipi.2015.9.511.en
dc.identifier.issn1930-8337en
dc.identifier.doi10.3934/ipi.2015.9.511en
dc.identifier.urihttp://hdl.handle.net/10754/597417en
dc.description.abstract© 2015 American Institute of Mathematical Sciences. In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with L2 data fitting term. We examine the properties of this model and we calculate exact solutions using simple piecewise affine functions as data terms. We investigate how these solutions behave with respect to the TGV parameters and we verify our results using numerical experiments.en
dc.description.sponsorshipThe first author was supported by UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis, the financial support provided by the EPSRC first grant Nr. EP/J009539/1 ''Sparse & Higher-order Image Restoration" and the Award No. KUK-I1007-43, made by King Abdullah University of Science and Technology (KAUST). The second author is supported by the Austrian Science Fund (FWF) under grant SFB32 (SFB ''Mathematical Optimization and Applications in the Biomedical Sciences").en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectDenoisingen
dc.subjectExact solutionsen
dc.subjectHigher order regularisationen
dc.subjectStaircasingen
dc.subjectTotal generalised variationen
dc.titleA study of the one dimensional total generalised variation regularisation problemen
dc.typeArticleen
dc.identifier.journalInverse Problems and Imagingen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionKarl-Franzens-Universitat Graz, Graz, Austriaen
kaust.grant.numberKUK-I1007-43en
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