Total Generalized Variation

Authors:
Kristian Bredies;Karl Kunisch;Thomas Pock
Affiliations:
kristian.bredies@uni-graz.at and karl.kunisch@uni-graz.at;-;pock@icg.tugraz.at
Venue:
SIAM Journal on Imaging Sciences
Year:
2010

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Abstract

The novel concept of total generalized variation of a function $u$ is introduced, and some of its essential properties are proved. Differently from the bounded variation seminorm, the new concept involves higher-order derivatives of $u$. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems. In particular this functional selectively regularizes on different regularity levels and, as a side effect, does not lead to a staircasing effect.