A Primal-Dual Approach for a Total Variation Wasserstein Flow

Martin Benning; Luca Calatroni; Bertram Düring; Carola-Bibiane Schönlieb

doi:10.1007/978-3-642-40020-9_45

A Primal-Dual Approach for a Total Variation Wasserstein Flow

Martin Benning, Luca Calatroni, Bertram Düring, Carola-Bibiane Schönlieb

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

5 Scopus citations

Abstract

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm. The constraint on the dual variable is relaxed by adding a penalty term, depending on a parameter that determines the weight of the penalisation. The paper is furnished with some numerical examples showing the denoising properties of the model considered. © 2013 Springer-Verlag.

Original language	English (US)
Title of host publication	Lecture Notes in Computer Science
Publisher	Springer Nature
Pages	413-421
Number of pages	9
ISBN (Print)	9783642400193
DOIs	https://doi.org/10.1007/978-3-642-40020-9_45
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: Carola-Bibiane Sch¨onlieb acknowledges financial supportprovided by the Cambridge Centre for Analysis (CCA), the Royal Society InternationalExchanges Award IE110314 for the project High-order CompressedSensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse& Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust SmallGrant on Non-smooth geometric reconstruction for high resolution MRI imagingof fluid transport in bed reactors. Further, this publication is based on worksupported by Award No. KUK-I1-007-43, made by King Abdullah University ofScience and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1007/978-3-642-40020-9_45

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abstract = "We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm. The constraint on the dual variable is relaxed by adding a penalty term, depending on a parameter that determines the weight of the penalisation. The paper is furnished with some numerical examples showing the denoising properties of the model considered. {\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: Carola-Bibiane Sch¨onlieb acknowledges financial supportprovided by the Cambridge Centre for Analysis (CCA), the Royal Society InternationalExchanges Award IE110314 for the project High-order CompressedSensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse& Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust SmallGrant on Non-smooth geometric reconstruction for high resolution MRI imagingof fluid transport in bed reactors. Further, this publication is based on worksupported by Award No. KUK-I1-007-43, made by King Abdullah University ofScience and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2013",

doi = "10.1007/978-3-642-40020-9_45",

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AU - Benning, Martin

AU - Calatroni, Luca

AU - Düring, Bertram

AU - Schönlieb, Carola-Bibiane

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: Carola-Bibiane Sch¨onlieb acknowledges financial supportprovided by the Cambridge Centre for Analysis (CCA), the Royal Society InternationalExchanges Award IE110314 for the project High-order CompressedSensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse& Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust SmallGrant on Non-smooth geometric reconstruction for high resolution MRI imagingof fluid transport in bed reactors. Further, this publication is based on worksupported by Award No. KUK-I1-007-43, made by King Abdullah University ofScience and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013

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N2 - We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm. The constraint on the dual variable is relaxed by adding a penalty term, depending on a parameter that determines the weight of the penalisation. The paper is furnished with some numerical examples showing the denoising properties of the model considered. © 2013 Springer-Verlag.

AB - We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm. The constraint on the dual variable is relaxed by adding a penalty term, depending on a parameter that determines the weight of the penalisation. The paper is furnished with some numerical examples showing the denoising properties of the model considered. © 2013 Springer-Verlag.

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SP - 413

EP - 421

BT - Lecture Notes in Computer Science

PB - Springer Nature

ER -

A Primal-Dual Approach for a Total Variation Wasserstein Flow

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