Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities

Handle URI:
http://hdl.handle.net/10754/597460
Title:
Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities
Authors:
Lenzen, Frank; Becker, Florian; Lellmann, Jan
Abstract:
Total variation (TV) regularization, originally introduced by Rudin, Osher and Fatemi in the context of image denoising, has become widely used in the field of inverse problems. Two major directions of modifications of the original approach were proposed later on. The first concerns adaptive variants of TV regularization, the second focuses on higher-order TV models. In the present paper, we combine the ideas of both directions by proposing adaptive second-order TV models, including one anisotropic model. Experiments demonstrate that introducing adaptivity results in an improvement of the reconstruction error. © 2013 Springer-Verlag.
Citation:
Lenzen F, Becker F, Lellmann J (2013) Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities. Scale Space and Variational Methods in Computer Vision: 61–73. Available: http://dx.doi.org/10.1007/978-3-642-38267-3_6.
Publisher:
Springer Science + Business Media
Journal:
Scale Space and Variational Methods in Computer Vision
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
2013
DOI:
10.1007/978-3-642-38267-3_6
Type:
Book Chapter
ISSN:
0302-9743; 1611-3349
Sponsors:
We thank Tanja Teuber and Kristian Bredies for kindlyproviding their codes. The work of J.L. was supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST),EPSRC first grant EP/J009539/1, and EPSRC/Isaac Newton Trust Small Grant.
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Full metadata record

DC FieldValue Language
dc.contributor.authorLenzen, Franken
dc.contributor.authorBecker, Florianen
dc.contributor.authorLellmann, Janen
dc.date.accessioned2016-02-25T12:40:10Zen
dc.date.available2016-02-25T12:40:10Zen
dc.date.issued2013en
dc.identifier.citationLenzen F, Becker F, Lellmann J (2013) Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities. Scale Space and Variational Methods in Computer Vision: 61–73. Available: http://dx.doi.org/10.1007/978-3-642-38267-3_6.en
dc.identifier.issn0302-9743en
dc.identifier.issn1611-3349en
dc.identifier.doi10.1007/978-3-642-38267-3_6en
dc.identifier.urihttp://hdl.handle.net/10754/597460en
dc.description.abstractTotal variation (TV) regularization, originally introduced by Rudin, Osher and Fatemi in the context of image denoising, has become widely used in the field of inverse problems. Two major directions of modifications of the original approach were proposed later on. The first concerns adaptive variants of TV regularization, the second focuses on higher-order TV models. In the present paper, we combine the ideas of both directions by proposing adaptive second-order TV models, including one anisotropic model. Experiments demonstrate that introducing adaptivity results in an improvement of the reconstruction error. © 2013 Springer-Verlag.en
dc.description.sponsorshipWe thank Tanja Teuber and Kristian Bredies for kindlyproviding their codes. The work of J.L. was supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST),EPSRC first grant EP/J009539/1, and EPSRC/Isaac Newton Trust Small Grant.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectadaptiveen
dc.subjectanisotropicen
dc.subjectdirectionalen
dc.subjectsecond-order total variationen
dc.subjectslope discontinuitiesen
dc.subjectTGVen
dc.subjectTVen
dc.titleAdaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuitiesen
dc.typeBook Chapteren
dc.identifier.journalScale Space and Variational Methods in Computer Visionen
dc.contributor.institutionHeidelberg Collaboratory for Image Processing, Heidelberg, Germanyen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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