Infimal Convolution Regularisation Functionals of BV and L$^{p}$ Spaces

Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)343-369
Number of pages27
JournalJournal of Mathematical Imaging and Vision
Volume55
Issue number3
DOIs
StatePublished - Feb 3 2016
Externally publishedYes

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