On semismooth Newton's methods for total variation minimization

Kwok Po NG; Liqun Qi; Yu Fei Yang; Yu Mei Huang

doi:10.1007/s10851-007-0650-0

On semismooth Newton's methods for total variation minimization

Kwok Po NG^*, Liqun Qi, Yu Fei Yang, Yu Mei Huang

^*Corresponding author for this work

Department of Mathematics

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

70 Citations (Scopus)

Abstract

In [2], Chambolle proposed an algorithm for minimizing the total variation of an image. In this short note, based on the theory on semismooth operators, we study semismooth Newton's methods for total variation minimization. The convergence and numerical results are also presented to show the effectiveness of the proposed algorithms.

Original language	English
Pages (from-to)	265-276
Number of pages	12
Journal	Journal of Mathematical Imaging and Vision
Volume	27
Issue number	3
DOIs	https://doi.org/10.1007/s10851-007-0650-0
Publication status	Published - Apr 2007

Scopus Subject Areas

Statistics and Probability
Modelling and Simulation
Condensed Matter Physics
Computer Vision and Pattern Recognition
Geometry and Topology
Applied Mathematics

User-Defined Keywords

Denoising
Regularization
Semismooth Newton's methods
Total variation

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10.1007/s10851-007-0650-0

Cite this

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title = "On semismooth Newton's methods for total variation minimization",

abstract = "In [2], Chambolle proposed an algorithm for minimizing the total variation of an image. In this short note, based on the theory on semismooth operators, we study semismooth Newton's methods for total variation minimization. The convergence and numerical results are also presented to show the effectiveness of the proposed algorithms.",

keywords = "Denoising, Regularization, Semismooth Newton's methods, Total variation",

author = "NG, {Kwok Po} and Liqun Qi and Yang, {Yu Fei} and Huang, {Yu Mei}",

note = "Funding Information: ∗The research of this author is supported in part by Hong Kong Research Grants Council Grant Nos. 7035/04P and 7035/05P, and HKBU FRGs. †The research of this author is supported in part by the Research Grant Council of Hong Kong. ‡This work was started while the author was visiting Department of Applied Mathematics, The Hong Kong Polytechnic University. The research of this author is supported in part by The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme and the National Science Foundation of China (No. 60572114).",

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doi = "10.1007/s10851-007-0650-0",

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AU - Huang, Yu Mei

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N2 - In [2], Chambolle proposed an algorithm for minimizing the total variation of an image. In this short note, based on the theory on semismooth operators, we study semismooth Newton's methods for total variation minimization. The convergence and numerical results are also presented to show the effectiveness of the proposed algorithms.

AB - In [2], Chambolle proposed an algorithm for minimizing the total variation of an image. In this short note, based on the theory on semismooth operators, we study semismooth Newton's methods for total variation minimization. The convergence and numerical results are also presented to show the effectiveness of the proposed algorithms.

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On semismooth Newton's methods for total variation minimization

Abstract

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