TY - GEN
T1 - Infimal convolution regularisation functionals of BV and Lp spaces. The case p = ∞
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.
UR - http://hdl.handle.net/10754/679383
UR - https://link.springer.com/10.1007/978-3-319-55795-3_15
UR - http://www.scopus.com/inward/record.url?scp=85018702279&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-55795-3_15
DO - 10.1007/978-3-319-55795-3_15
M3 - Conference contribution
SN - 9783319557946
SP - 169
EP - 179
BT - IFIP Advances in Information and Communication Technology
PB - Springer International Publishing
ER -