On a weighted total variation minimization problem |
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Authors: | Guillaume Carlier |
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Institution: | a CEREMADE, Université Paris Dauphine, France b Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, France |
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Abstract: | 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 modeling. 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. |
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Keywords: | Generalized Cheeger sets Total variation minimization |
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