Alternating direction method of multipliers for nonconvex log total variation image restoration

Benxin ZHANG; Guopu ZHU; Zhibin ZHU; Sam KWONG

doi:10.1016/j.apm.2022.09.018

Alternating direction method of multipliers for nonconvex log total variation image restoration

Benxin ZHANG, Guopu ZHU, Zhibin ZHU, Sam KWONG

Research output: Journal Publications › Journal Article (refereed) › peer-review

13 Citations (Scopus)

Abstract

In this paper, we propose a nonconvex log total variation model for image restoration. A specific alternating direction method of multipliers is also presented to solve the nonconvex optimization model. Under mild conditions, we prove that the sequence generated by the proposed alternating direction method of multipliers converges to a stationary point. Experiment results on image denoising, image deblurring, computed tomography, magnetic resonance imaging and image super-resolution demonstrate that the proposed method is effective and improves the quality of image recovery.

Original language	English
Pages (from-to)	338-359
Number of pages	22
Journal	Applied Mathematical Modelling
Volume	114
Early online date	30 Sept 2022
DOIs	https://doi.org/10.1016/j.apm.2022.09.018
Publication status	Published - Feb 2023
Externally published	Yes

Bibliographical note

Funding Information:
We are grateful to the editor and anonymous reviewers for their valuable comments which help to improve the presentation of the paper. This work was supported in part by the National Natural Science Foundation of China under Grant 11901137, Grant 62172402, Grant 61872350, and Grant 61967004, in part by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), in part by the Hong Kong RGC GRF under Grant 9042816 (CityU 11209819) and Grant 9042958 (CityU 11203820), and in part by the Fundamental Research Funds for the Central Universities under Grant FRFCU5710011322.

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Alternating direction method of multipliers
Convergence
Image restoration
Log total variation
Nonconvex optimization

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10.1016/j.apm.2022.09.018

Cite this

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title = "Alternating direction method of multipliers for nonconvex log total variation image restoration",

abstract = "In this paper, we propose a nonconvex log total variation model for image restoration. A specific alternating direction method of multipliers is also presented to solve the nonconvex optimization model. Under mild conditions, we prove that the sequence generated by the proposed alternating direction method of multipliers converges to a stationary point. Experiment results on image denoising, image deblurring, computed tomography, magnetic resonance imaging and image super-resolution demonstrate that the proposed method is effective and improves the quality of image recovery.",

keywords = "Alternating direction method of multipliers, Convergence, Image restoration, Log total variation, Nonconvex optimization",

author = "Benxin ZHANG and Guopu ZHU and Zhibin ZHU and Sam KWONG",

note = "Funding Information: We are grateful to the editor and anonymous reviewers for their valuable comments which help to improve the presentation of the paper. This work was supported in part by the National Natural Science Foundation of China under Grant 11901137, Grant 62172402, Grant 61872350, and Grant 61967004, in part by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), in part by the Hong Kong RGC GRF under Grant 9042816 (CityU 11209819) and Grant 9042958 (CityU 11203820), and in part by the Fundamental Research Funds for the Central Universities under Grant FRFCU5710011322. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2023",

month = feb,

doi = "10.1016/j.apm.2022.09.018",

language = "English",

volume = "114",

pages = "338--359",

journal = "Applied Mathematical Modelling",

issn = "0307-904X",

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TY - JOUR

T1 - Alternating direction method of multipliers for nonconvex log total variation image restoration

AU - ZHANG, Benxin

AU - ZHU, Guopu

AU - ZHU, Zhibin

AU - KWONG, Sam

N1 - Funding Information: We are grateful to the editor and anonymous reviewers for their valuable comments which help to improve the presentation of the paper. This work was supported in part by the National Natural Science Foundation of China under Grant 11901137, Grant 62172402, Grant 61872350, and Grant 61967004, in part by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA), in part by the Hong Kong RGC GRF under Grant 9042816 (CityU 11209819) and Grant 9042958 (CityU 11203820), and in part by the Fundamental Research Funds for the Central Universities under Grant FRFCU5710011322. Publisher Copyright: © 2022 Elsevier Inc.

PY - 2023/2

Y1 - 2023/2

N2 - In this paper, we propose a nonconvex log total variation model for image restoration. A specific alternating direction method of multipliers is also presented to solve the nonconvex optimization model. Under mild conditions, we prove that the sequence generated by the proposed alternating direction method of multipliers converges to a stationary point. Experiment results on image denoising, image deblurring, computed tomography, magnetic resonance imaging and image super-resolution demonstrate that the proposed method is effective and improves the quality of image recovery.

AB - In this paper, we propose a nonconvex log total variation model for image restoration. A specific alternating direction method of multipliers is also presented to solve the nonconvex optimization model. Under mild conditions, we prove that the sequence generated by the proposed alternating direction method of multipliers converges to a stationary point. Experiment results on image denoising, image deblurring, computed tomography, magnetic resonance imaging and image super-resolution demonstrate that the proposed method is effective and improves the quality of image recovery.

KW - Alternating direction method of multipliers

KW - Convergence

KW - Image restoration

KW - Log total variation

KW - Nonconvex optimization

UR - http://www.scopus.com/inward/record.url?scp=85139835313&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2022.09.018

DO - 10.1016/j.apm.2022.09.018

M3 - Journal Article (refereed)

SN - 0307-904X

VL - 114

SP - 338

EP - 359

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -

Alternating direction method of multipliers for nonconvex log total variation image restoration

Abstract

Bibliographical note

Keywords

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Adaptive Dynamic Range Enhancement Oriented to High Dynamic Display (面向高動態顯示的自適應動態範圍增強)

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Alternating direction method of multipliers for nonconvex log total variation image restoration

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

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Adaptive Dynamic Range Enhancement Oriented to High Dynamic Display (面向高動態顯示的自適應動態範圍增強)

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