PIECEWISE CONSTANT PROFILES MINIMIZING TOTAL VARIATION ENERGIES OF KOBAYASHI-WARREN-CARTER TYPE WITH FIDELITY

GIGA, YOSHIKAZU; KUBO, AYATO; KURODA, HIROTOSHI; OKAMOTO, JUN; SAKAKIBARA, KOYA

doi:https://doi.org/10.14943/111244

PIECEWISE CONSTANT PROFILES MINIMIZING TOTAL VARIATION ENERGIES OF KOBAYASHI-WARREN-CARTER TYPE WITH FIDELITY

GIGA, YOSHIKAZU; KUBO, AYATO; KURODA, HIROTOSHI et al.

Hokkaido University Preprint Series in Mathematics, 2024, 1159, 1-43

Permalink : https://doi.org/10.14943/111244

このアイテムのアクセス数:253件（2026-08-10 20:41 集計）

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アクセス権	open access
DOI	https://doi.org/10.14943/111244
URI	https://hdl.handle.net/2115/92979
タイトル	PIECEWISE CONSTANT PROFILES MINIMIZING TOTAL VARIATION ENERGIES OF KOBAYASHI-WARREN-CARTER TYPE WITH FIDELITY
著者	GIGA, YOSHIKAZU ; KUBO, AYATO ; KURODA, HIROTOSHI ; OKAMOTO, JUN ; SAKAKIBARA, KOYA
e-Rad_Researcher 70144110 著者名 GIGA, YOSHIKAZU
著者名 KUBO, AYATO
e-Rad_Researcher 80635657 著者名 KURODA, HIROTOSHI
著者名 OKAMOTO, JUN
e-Rad_Researcher 30807772 著者名 SAKAKIBARA, KOYA
言語	英語
発行日	2024-08-23
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1159
ページ	1-43
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record