Average-distance problem with curvature penalization for data parameterization: regularity of minimizers

We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functional to measure the quality of the approximation and penalizes the curvature, similarly to the elastica functional. Intro...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 27; p. 8
Main Authors Lu, Xin Yang, Slepčev, Dejan
Format Journal Article
LanguageEnglish
Published 2021
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Summary:We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functional to measure the quality of the approximation and penalizes the curvature, similarly to the elastica functional. Introducing the curvature penalization overcomes some of the shortcomings of the average-distance functional, in particular the lack of regularity of minimizers. We establish existence, uniqueness and regularity of minimizers of the proposed functional. In particular we establish C 1,1 estimates on the minimizers.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2021002