High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration

High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration

In this paper, a new model for image restoration under Poisson noise based on a high-order total bounded variation is proposed. Existence and uniqueness of its solution are proved. To find the global optimal solution of our strongly convex model, a split Bregman algorithm is introduced. Furthermore,...

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Main Authors: Jun Zhang, Mingxi Ma, Zhaoming Wu, Chengzhi Deng
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/2502731
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spelling doaj-b1d8f7e7b4e245fba736bd26551317e22020-11-25T00:28:38ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/25027312502731High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image RestorationJun Zhang0Mingxi Ma1Zhaoming Wu2Chengzhi Deng3Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, ChinaCollege of Science, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, ChinaJiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, ChinaJiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, ChinaIn this paper, a new model for image restoration under Poisson noise based on a high-order total bounded variation is proposed. Existence and uniqueness of its solution are proved. To find the global optimal solution of our strongly convex model, a split Bregman algorithm is introduced. Furthermore, a rigorous convergence theory of the proposed algorithm is established. Experimental results are provided to demonstrate the effectiveness and efficiency of the proposed method over the classic total bounded variation-based model.http://dx.doi.org/10.1155/2019/2502731
collection DOAJ
language English
format Article
sources DOAJ
author Jun Zhang
Mingxi Ma
Zhaoming Wu
Chengzhi Deng
spellingShingle Jun Zhang
Mingxi Ma
Zhaoming Wu
Chengzhi Deng
High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration
Mathematical Problems in Engineering
author_facet Jun Zhang
Mingxi Ma
Zhaoming Wu
Chengzhi Deng
author_sort Jun Zhang
title High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration
title_short High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration
title_full High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration
title_fullStr High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration
title_full_unstemmed High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration
title_sort high-order total bounded variation model and its fast algorithm for poissonian image restoration
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description In this paper, a new model for image restoration under Poisson noise based on a high-order total bounded variation is proposed. Existence and uniqueness of its solution are proved. To find the global optimal solution of our strongly convex model, a split Bregman algorithm is introduced. Furthermore, a rigorous convergence theory of the proposed algorithm is established. Experimental results are provided to demonstrate the effectiveness and efficiency of the proposed method over the classic total bounded variation-based model.
url http://dx.doi.org/10.1155/2019/2502731
work_keys_str_mv AT junzhang highordertotalboundedvariationmodelanditsfastalgorithmforpoissonianimagerestoration
AT mingxima highordertotalboundedvariationmodelanditsfastalgorithmforpoissonianimagerestoration
AT zhaomingwu highordertotalboundedvariationmodelanditsfastalgorithmforpoissonianimagerestoration
AT chengzhideng highordertotalboundedvariationmodelanditsfastalgorithmforpoissonianimagerestoration
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