Numerical computations of split Bregman method for fourth order total variation flow

Yoshikazu Giga; Yuki Ueda

doi:10.1016/j.jcp.2019.109114

Numerical computations of split Bregman method for fourth order total variation flow

Yoshikazu Giga, Yuki Ueda^*

^*Corresponding author for this work

Waseda Research Institute for Science and Engineering

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The split Bregman framework for Osher-Solé-Vese (OSV) model and fourth order total variation flow are studied. We discretize the problem by piecewise constant function and compute ∇(−Δ_av)⁻¹ approximately and exactly. Furthermore, we provide a new shrinkage operator for Spohn's fourth order model. Numerical experiments are demonstrated for fourth order problems under periodic boundary condition.

Original language	English
Article number	109114
Journal	Journal of Computational Physics
Volume	405
DOIs	https://doi.org/10.1016/j.jcp.2019.109114
Publication status	Published - 2020 Mar 15

Keywords

Fourth order model
Osher-Solé-Vese model
Singular diffusion
Split Bregman
Surface relaxation
Total variation flow

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2019.109114

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title = "Numerical computations of split Bregman method for fourth order total variation flow",

abstract = "The split Bregman framework for Osher-Sol{\'e}-Vese (OSV) model and fourth order total variation flow are studied. We discretize the problem by piecewise constant function and compute ∇(−Δav)−1 approximately and exactly. Furthermore, we provide a new shrinkage operator for Spohn's fourth order model. Numerical experiments are demonstrated for fourth order problems under periodic boundary condition.",

keywords = "Fourth order model, Osher-Sol{\'e}-Vese model, Singular diffusion, Split Bregman, Surface relaxation, Total variation flow",

author = "Yoshikazu Giga and Yuki Ueda",

note = "Funding Information: A part of the work of the second author was done when he was a postdoc fellow at the University of Tokyo. Its hospitality is gratefully acknowledged. The work of the first author was partly supported by the Japan Society for the Promotion of Science through the grant No. 26220702 (Kiban S), No. 19H00639 (Kiban A), No. 18H05323 (Kaitaku), No. 17H01091 (Kiban A) and No. 16H03948 (Kiban B). Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = mar,

day = "15",

doi = "10.1016/j.jcp.2019.109114",

language = "English",

volume = "405",

journal = "Journal of Computational Physics",

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T1 - Numerical computations of split Bregman method for fourth order total variation flow

AU - Giga, Yoshikazu

AU - Ueda, Yuki

N1 - Funding Information: A part of the work of the second author was done when he was a postdoc fellow at the University of Tokyo. Its hospitality is gratefully acknowledged. The work of the first author was partly supported by the Japan Society for the Promotion of Science through the grant No. 26220702 (Kiban S), No. 19H00639 (Kiban A), No. 18H05323 (Kaitaku), No. 17H01091 (Kiban A) and No. 16H03948 (Kiban B). Publisher Copyright: © 2019 Elsevier Inc.

PY - 2020/3/15

Y1 - 2020/3/15

N2 - The split Bregman framework for Osher-Solé-Vese (OSV) model and fourth order total variation flow are studied. We discretize the problem by piecewise constant function and compute ∇(−Δav)−1 approximately and exactly. Furthermore, we provide a new shrinkage operator for Spohn's fourth order model. Numerical experiments are demonstrated for fourth order problems under periodic boundary condition.

AB - The split Bregman framework for Osher-Solé-Vese (OSV) model and fourth order total variation flow are studied. We discretize the problem by piecewise constant function and compute ∇(−Δav)−1 approximately and exactly. Furthermore, we provide a new shrinkage operator for Spohn's fourth order model. Numerical experiments are demonstrated for fourth order problems under periodic boundary condition.

KW - Fourth order model

KW - Osher-Solé-Vese model

KW - Singular diffusion

KW - Split Bregman

KW - Surface relaxation

KW - Total variation flow

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DO - 10.1016/j.jcp.2019.109114

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 109114

ER -

Numerical computations of split Bregman method for fourth order total variation flow

Abstract

Keywords

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