Infimal convolution regularisation functionals of BV and Lp spaces. The case p = ∞

Martin Burger; Konstantinos Papafitsoros; Evangelos Papoutsellis; Carola Bibiane Schönlieb

doi:10.1007/978-3-319-55795-3_15

Infimal convolution regularisation functionals of BV and Lp spaces. The case p = ∞

Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis, Carola Bibiane Schönlieb

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

7 Scopus citations

Abstract

In this paper we analyse an infimal convolution type regularisation functional called TVL∞ , based on the total variation (TV) and the L ∞ norm of the gradient. The functional belongs to a more general family of TVLp functionals (1 < p ≤ ∞) introduced in [5]. There, the case 1 < p < ∞ is examined while here we focus on the p = ∞ case. We show via analytical and numerical results that the minimisation of the TVL∞ functional promotes piecewise affine structures in the reconstructed images similar to the state of the art total generalised variation (TGV) but improving upon preservation of hat–like structures. We also propose a spatially adapted version of our model that produces results comparable to TGV and allows space for further improvement.

Original language	English (US)
Title of host publication	IFIP Advances in Information and Communication Technology
Publisher	Springer International Publishing
Pages	169-179
Number of pages	11
ISBN (Print)	9783319557946
DOIs	https://doi.org/10.1007/978-3-319-55795-3_15
State	Published - Apr 2 2017
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-28
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: The authors acknowledge support of the Royal Society International Exchange Award Nr. IE110314. This work is further supported by the King Abdullah University for Science and Technology (KAUST) Award No. KUK-I1-007-43, the EPSRC first grant Nr. EP/J009539/1 and the EPSRC grant Nr. EP/M00483X/1. MB acknowledges further support by ERC via Grant EU FP 7-ERC Consolidator Grant 615216 LifeInverse. KP acknowledges the financial support of EPSRC and the Alexander von Humboldt Foundation while in UK and Germany respectively. EP acknowledges support by Jesus College, Cambridge and Embiricos Trust.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Information Systems and Management

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10.1007/978-3-319-55795-3_15

Cite this

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title = "Infimal convolution regularisation functionals of BV and Lp spaces. The case p = ∞",

abstract = "In this paper we analyse an infimal convolution type regularisation functional called TVL∞ , based on the total variation (TV) and the L ∞ norm of the gradient. The functional belongs to a more general family of TVLp functionals (1 < p ≤ ∞) introduced in [5]. There, the case 1 < p < ∞ is examined while here we focus on the p = ∞ case. We show via analytical and numerical results that the minimisation of the TVL∞ functional promotes piecewise affine structures in the reconstructed images similar to the state of the art total generalised variation (TGV) but improving upon preservation of hat–like structures. We also propose a spatially adapted version of our model that produces results comparable to TGV and allows space for further improvement.",

author = "Martin Burger and Konstantinos Papafitsoros and Evangelos Papoutsellis and Sch{\"o}nlieb, {Carola Bibiane}",

note = "KAUST Repository Item: Exported on 2022-06-28 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: The authors acknowledge support of the Royal Society International Exchange Award Nr. IE110314. This work is further supported by the King Abdullah University for Science and Technology (KAUST) Award No. KUK-I1-007-43, the EPSRC first grant Nr. EP/J009539/1 and the EPSRC grant Nr. EP/M00483X/1. MB acknowledges further support by ERC via Grant EU FP 7-ERC Consolidator Grant 615216 LifeInverse. KP acknowledges the financial support of EPSRC and the Alexander von Humboldt Foundation while in UK and Germany respectively. EP acknowledges support by Jesus College, Cambridge and Embiricos Trust. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Burger, Martin

AU - Papafitsoros, Konstantinos

AU - Papoutsellis, Evangelos

AU - Schönlieb, Carola Bibiane

N1 - KAUST Repository Item: Exported on 2022-06-28 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: The authors acknowledge support of the Royal Society International Exchange Award Nr. IE110314. This work is further supported by the King Abdullah University for Science and Technology (KAUST) Award No. KUK-I1-007-43, the EPSRC first grant Nr. EP/J009539/1 and the EPSRC grant Nr. EP/M00483X/1. MB acknowledges further support by ERC via Grant EU FP 7-ERC Consolidator Grant 615216 LifeInverse. KP acknowledges the financial support of EPSRC and the Alexander von Humboldt Foundation while in UK and Germany respectively. EP acknowledges support by Jesus College, Cambridge and Embiricos Trust. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2017/4/2

Y1 - 2017/4/2

N2 - In this paper we analyse an infimal convolution type regularisation functional called TVL∞ , based on the total variation (TV) and the L ∞ norm of the gradient. The functional belongs to a more general family of TVLp functionals (1 < p ≤ ∞) introduced in [5]. There, the case 1 < p < ∞ is examined while here we focus on the p = ∞ case. We show via analytical and numerical results that the minimisation of the TVL∞ functional promotes piecewise affine structures in the reconstructed images similar to the state of the art total generalised variation (TGV) but improving upon preservation of hat–like structures. We also propose a spatially adapted version of our model that produces results comparable to TGV and allows space for further improvement.

AB - In this paper we analyse an infimal convolution type regularisation functional called TVL∞ , based on the total variation (TV) and the L ∞ norm of the gradient. The functional belongs to a more general family of TVLp functionals (1 < p ≤ ∞) introduced in [5]. There, the case 1 < p < ∞ is examined while here we focus on the p = ∞ case. We show via analytical and numerical results that the minimisation of the TVL∞ functional promotes piecewise affine structures in the reconstructed images similar to the state of the art total generalised variation (TGV) but improving upon preservation of hat–like structures. We also propose a spatially adapted version of our model that produces results comparable to TGV and allows space for further improvement.

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DO - 10.1007/978-3-319-55795-3_15

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BT - IFIP Advances in Information and Communication Technology

PB - Springer International Publishing

ER -

Infimal convolution regularisation functionals of BV and Lp spaces. The case p = ∞

Abstract

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