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 proceedingChapter

5 Scopus citations


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 languageEnglish (US)
Title of host publicationLecture Notes in Computer Science
PublisherSpringer Nature
Number of pages9
ISBN (Print)9783642400193
StatePublished - 2013
Externally publishedYes

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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