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

被引：17

作者：

Zhang, Benxin ^{[1
]}

Zhu, Guopu ^{[2
]}

Zhu, Zhibin ^{[3
]}

Kwong, Sam ^{[4
,5
]}

机构：

[1] Guilin Univ Elect Technol, Sch Elect Engn & Automat, Guangxi Key Lab Automat Detecting Technol & Instru, Guilin 541004, Peoples R China

[2] Harbin Inst Technol, Sch Comp Sci & Technol, Harbin 150001, Peoples R China

[3] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guangxi Coll & Univ Key Lab Data Anal & Computat, Guilin 541004, Peoples R China

[4] City Univ Hong Kong, Dept Comp Sci, Hong Kong 999077, Peoples R China

[5] City Univ Hong Kong, Shenzhen Res Inst, Shenzhen 518057, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2023年 / 114卷

基金：

中国国家自然科学基金;

关键词：

Image restoration; Log total variation; Alternating direction method of multipliers; Nonconvex optimization; Convergence; COMPUTED-TOMOGRAPHY; RECONSTRUCTION; MINIMIZATION; MODEL; OPTIMIZATION; SELECTION; REMOVAL; NOISE;

D O I：

10.1016/j.apm.2022.09.018

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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 noncon-vex 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.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：338 / 359

页数：22

共 57 条

[1]

[Anonymous], 1983, Augmented Lagrangian Methods: Applications to the Solution of Boundary-Value Problems

[2] Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality [J].

Attouch, Hedy ;

Bolte, Jerome ;

Redont, Patrick ;

Soubeyran, Antoine .

MATHEMATICS OF OPERATIONS RESEARCH, 2010, 35 (02) :438-457

[3]

Bauschke HH, 2011, CMS BOOKS MATH, P1, DOI 10.1007/978-1-4419-9467-7

[4] TIGRE: a MATLAB-GPU toolbox for CBCT image reconstruction [J].

Biguri, Ander ;

Dosanjh, Manjit ;

Hancock, Steven ;

Soleimani, Manuchehr .

BIOMEDICAL PHYSICS & ENGINEERING EXPRESS, 2016, 2 (05)

[5] Proximal alternating linearized minimization for nonconvex and nonsmooth problems [J].

Bolte, Jerome ;

Sabach, Shoham ;

Teboulle, Marc .

MATHEMATICAL PROGRAMMING, 2014, 146 (1-2) :459-494

[6] A generalized Gaussian image model for edge-preserving MAP estimation [J].

Bournan, Charles ;

Sauer, Ken .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 1993, 2 (03) :296-310

[7] Distributed optimization and statistical learning via the alternating direction method of multipliers [J].

Boyd S. ;

Parikh N. ;

Chu E. ;

Peleato B. ;

Eckstein J. .

Foundations and Trends in Machine Learning, 2010, 3 (01) :1-122

[8] Enhancing Sparsity by Reweighted l1 Minimization [J].

Candes, Emmanuel J. ;

Wakin, Michael B. ;

Boyd, Stephen P. .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2008, 14 (5-6) :877-905

[9] Efficient l0 Gradient-Based Super-Resolution for Simplified Image Segmentation [J].

Cascarano, Pasquale ;

Calatroni, Luca ;

Piccolomini, Elena Loli .

IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING, 2021, 7 :399-408

[10] A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging [J].

Chambolle, Antonin ;

Pock, Thomas .

JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2011, 40 (01) :120-145

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