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Hokkaido University Preprint Series in Mathematics >
A duality based approach to the minimizing total variation flow in the space H-s
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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 Hs (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
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Submitter: 数学紀要登録作業用
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