Piecewise constant profiles minimizing total variation energies of Kobayashi-Warren-Carter type with fidelity
| Autor: | Giga, Yoshikazu, Kubo, Ayato, Kuroda, Hirotoshi, Okamoto, Jun, Sakakibara, Koya |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider a total variation type energy which measures the jump discontinuities different from usual total variation energy. Such a type of energy is obtained as a singular limit of the Kobayashi-Warren-Carter energy with minimization with respect to the order parameter. We consider the Rudin-Osher-Fatemi type energy by replacing relaxation term by this type of total variation energy. We show that all minimizers are piecewise constant if the data is continuous in one-dimensional setting. Moreover, the number of jumps is bounded by an explicit constant involving a constant related to the fidelity. This is quite different from conventional Rudin-Osher-Fatemi energy where a minimizer must have no jump if the data has no jumps. The existence of a minimizer is guaranteed in multi-dimensional setting when the data is bounded. Comment: 43 pages, 11 figures |
| Databáze: | arXiv |
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