On a weighted total variation minimization problem
Comte, Myriam; Carlier, Guillaume (2007), On a weighted total variation minimization problem, Journal of Functional Analysis, 250, 1, p. 214-226. http://dx.doi.org/10.1016/j.jfa.2007.05.022
TypeArticle accepté pour publication ou publié
Journal nameJournal of Functional Analysis
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Abstract (EN)The present article is devoted to the study of a constrained weighted total variation minimization problem, which may be viewed as a relaxation of a generalized Cheeger problem and is motivated by landslide modelling. Using the fact that the set of minimizers is invariant by a wide class of monotone transformations, we prove that level sets of minimizers are generalized Cheeger sets and obtain qualitative properties of the minimizers: they are all bounded and all achieve their essential supremum on a set of positive measure.
Subjects / KeywordsGeneralized Cheeger sets; Total variation minimization
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