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

Frank Lenzen; Florian Becker; Jan Lellmann

doi:10.1007/978-3-642-38267-3_6

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

Frank Lenzen, Florian Becker, Jan Lellmann

Research output: Chapter in Book/Report/Conference proceeding › Chapter

13 Scopus citations

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.

Original language	English (US)
Title of host publication	Scale Space and Variational Methods in Computer Vision
Publisher	Springer Nature
Pages	61-73
Number of pages	13
ISBN (Print)	9783642382666
DOIs	https://doi.org/10.1007/978-3-642-38267-3_6
State	Published - 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1007/978-3-642-38267-3_6

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title = "Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities",

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. {\textcopyright} 2013 Springer-Verlag.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Becker, Florian

AU - Lellmann, Jan

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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AB - 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.

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BT - Scale Space and Variational Methods in Computer Vision

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ER -

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

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