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

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

26 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
Journal	Applied Mathematical Modelling
Volume	114
Online published	30 Sept 2022
DOIs	https://doi.org/10.1016/j.apm.2022.09.018
Publication status	Published - Feb 2023

Funding

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.

Research Keywords

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

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RGC-funded

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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",

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",

publisher = "Elsevier Inc.",

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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

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

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85139835313&origin=recordpage

U2 - 10.1016/j.apm.2022.09.018

DO - 10.1016/j.apm.2022.09.018

M3 - RGC 21 - Publication in refereed journal

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

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Research Keywords

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GRF: Adaptive Dynamic Range Enhancement Oriented to High Dynamic Display

GRF: Intelligent Ultra High Definition Video Encoder Optimization for Future Versatile Video Coding

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

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

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Other Files and Links

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GRF: Adaptive Dynamic Range Enhancement Oriented to High Dynamic Display

GRF: Intelligent Ultra High Definition Video Encoder Optimization for Future Versatile Video Coding

Cite this