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 proceedingConference contribution

6 Scopus citations


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 languageEnglish (US)
Title of host publicationIFIP Advances in Information and Communication Technology
PublisherSpringer International Publishing
Number of pages11
ISBN (Print)9783319557946
StatePublished - Apr 2 2017
Externally publishedYes

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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