Piecewise constant profiles minimizing total variation energies of Kobayashi-Warren-Carter type with fidelity

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-Oshe...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Giga, Yoshikazu, Kubo, Ayato, Kuroda, Hirotoshi, Okamoto, Jun, Sakakibara, Koya
Format: Article
Language:English
Subjects:
Accuracy
Order parameters
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422