dc.contributor.author Burger, Martin dc.contributor.author Papafitsoros, Konstantinos dc.contributor.author Papoutsellis, Evangelos dc.contributor.author Schönlieb, Carola-Bibiane dc.date.accessioned 2017-05-15T10:35:08Z dc.date.available 2017-05-15T10:35:08Z dc.date.issued 2016-02-03 dc.identifier.citation Burger M, Papafitsoros K, Papoutsellis E, Schönlieb C-B (2016) Infimal Convolution Regularisation Functionals of BV and Lp Spaces. Journal of Mathematical Imaging and Vision 55: 343–369. Available: http://dx.doi.org/10.1007/s10851-015-0624-6. dc.identifier.issn 0924-9907 dc.identifier.issn 1573-7683 dc.identifier.doi 10.1007/s10851-015-0624-6 dc.identifier.uri http://hdl.handle.net/10754/623558 dc.description.abstract We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation seminorm and Lp norms. A unified well-posedness analysis is presented and a detailed study of the one-dimensional model is performed, by computing exact solutions for the corresponding denoising problem and the case p=2. Furthermore, the dependency of the regularisation properties of this infimal convolution approach to the choice of p is studied. It turns out that in the case p=2 this regulariser is equivalent to the Huber-type variant of total variation regularisation. We provide numerical examples for image decomposition as well as for image denoising. We show that our model is capable of eliminating the staircasing effect, a well-known disadvantage of total variation regularisation. Moreover as p increases we obtain almost piecewise affine reconstructions, leading also to a better preservation of hat-like structures. dc.description.sponsorship The authors would like to thank the anonymous reviewers for their interesting comments and suggestions which especially motivated our more detailed discussion on the generalised Huber total variation functional. The authors acknowledge support of the Royal Society International Exchange Award No. 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 No. EP/J009539/1 and the EPSRC Grant No. 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 Scholarship. dc.publisher Springer Nature dc.subject Total Variation dc.subject Infimal convolution dc.subject Denoising dc.subject Staircasing dc.subject Lp norms dc.subject Image decomposition dc.title Infimal Convolution Regularisation Functionals of BV and L$^{p}$ Spaces dc.type Article dc.identifier.journal Journal of Mathematical Imaging and Vision dc.contributor.institution Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany dc.contributor.institution Institute for Mathematics, Humboldt University of Berlin, Berlin, Germany dc.contributor.institution Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK kaust.grant.number KUK-I1-007-43 dc.date.published-online 2016-02-03 dc.date.published-print 2016-07
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