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A duality based approach to the minimizing total variation flow in the space H-s

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84246

Title: A duality based approach to the minimizing total variation flow in the space H-s
Authors: GIGA, YOSHIKAZU Browse this author
Muszkieta, Monika Browse this author
Rybka, Piotr Browse this author
Keywords: total variation
Rudin-Osher-Fatemi model
fractional Sobolev spaces,negative Sobolev spaces.
Issue Date: 16-Jun-2017
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1102
Start Page: 1
End Page: 24
Abstract: We consider a gradient ow of the total variation in a negative Sobolev space H􀀀s (0 s 1) under the periodic boundary condition. If s = 0, the ow is nothing but the classical total variation ow. If s = 1, this is the fourth order total variation ow. We consider a convex variational problem which gives an implicit-time discrete scheme for the ow. By a duality based method, we give a simple numerical scheme to calculate this minimizing problem numerically and discuss convergence of a forward- backward splitting scheme. Several numerical experiments are given.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69906
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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