Domain decomposition method for image deblurring

Jing Xu; Hui Bin Chang; Jing Qin

doi:10.1016/j.cam.2014.03.030

Domain decomposition method for image deblurring

Jing Xu, Hui Bin Chang, Jing Qin

Research output: Contribution to journal › Review article › peer-review

13 Scopus citations

Abstract

As a fundamental problem in image processing, image deblurring has still attracted a lot of research attention. Due to the large computational cost, especially for high-resolution images, it becomes challenging to solve the deblurring minimization problem and the underlying partial differential equations. The domain decomposition method (DD), as one of the most efficient algorithms for solving large scale problems, had not been applied directly to image deblurring because of the global characteristic of the blur operator. In this paper, in order to avoid separating the blur operator, we propose an algorithm for directly solving the total variational based minimization problems with DD. Various numerical experiments and comparisons demonstrate that the larger the image size is, the more efficient the proposed method is in saving running time. The parallelization has also been realized by using the parallel computing toolbox of MATLAB.

Original language	English
Pages (from-to)	401-414
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	271
DOIs	https://doi.org/10.1016/j.cam.2014.03.030
State	Published - Dec 1 2014

Bibliographical note

Funding Information:
This research is supported by Singapore MOE Grant T207B2202 , and Singapore NRF 2007IDM-IDM002-010 . The research of the first author is also partially supported by Youth Foundation of NSFC with Grant Nos. 11001239 , 11101365 , and 11201420 . The second author is partially supported by PHD Programme 52XB1304 of Tianjin Normal University and NSFC with Grant No. 11071080 .

Funding

This research is supported by Singapore MOE Grant T207B2202 , and Singapore NRF 2007IDM-IDM002-010 . The research of the first author is also partially supported by Youth Foundation of NSFC with Grant Nos. 11001239 , 11101365 , and 11201420 . The second author is partially supported by PHD Programme 52XB1304 of Tianjin Normal University and NSFC with Grant No. 11071080 .

Funders	Funder number
Youth Foundation of NSFC	11101365, 52XB1304, 11201420, 11001239
Danish National Research Foundation	2007IDM-IDM002-010
Ministry of Education - Singapore	T207B2202
National Natural Science Foundation of China (NSFC)	11071080
Tianjin Normal University

Keywords

Image deblurring
Overlapping domain decomposition
Total variation minimization

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2014.03.030

Cite this

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title = "Domain decomposition method for image deblurring",

abstract = "As a fundamental problem in image processing, image deblurring has still attracted a lot of research attention. Due to the large computational cost, especially for high-resolution images, it becomes challenging to solve the deblurring minimization problem and the underlying partial differential equations. The domain decomposition method (DD), as one of the most efficient algorithms for solving large scale problems, had not been applied directly to image deblurring because of the global characteristic of the blur operator. In this paper, in order to avoid separating the blur operator, we propose an algorithm for directly solving the total variational based minimization problems with DD. Various numerical experiments and comparisons demonstrate that the larger the image size is, the more efficient the proposed method is in saving running time. The parallelization has also been realized by using the parallel computing toolbox of MATLAB.",

keywords = "Image deblurring, Overlapping domain decomposition, Total variation minimization",

author = "Jing Xu and Chang, {Hui Bin} and Jing Qin",

note = "Funding Information: This research is supported by Singapore MOE Grant T207B2202 , and Singapore NRF 2007IDM-IDM002-010 . The research of the first author is also partially supported by Youth Foundation of NSFC with Grant Nos. 11001239 , 11101365 , and 11201420 . The second author is partially supported by PHD Programme 52XB1304 of Tianjin Normal University and NSFC with Grant No. 11071080 . ",

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doi = "10.1016/j.cam.2014.03.030",

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AU - Xu, Jing

AU - Chang, Hui Bin

AU - Qin, Jing

N1 - Funding Information: This research is supported by Singapore MOE Grant T207B2202 , and Singapore NRF 2007IDM-IDM002-010 . The research of the first author is also partially supported by Youth Foundation of NSFC with Grant Nos. 11001239 , 11101365 , and 11201420 . The second author is partially supported by PHD Programme 52XB1304 of Tianjin Normal University and NSFC with Grant No. 11071080 .

PY - 2014/12/1

Y1 - 2014/12/1

N2 - As a fundamental problem in image processing, image deblurring has still attracted a lot of research attention. Due to the large computational cost, especially for high-resolution images, it becomes challenging to solve the deblurring minimization problem and the underlying partial differential equations. The domain decomposition method (DD), as one of the most efficient algorithms for solving large scale problems, had not been applied directly to image deblurring because of the global characteristic of the blur operator. In this paper, in order to avoid separating the blur operator, we propose an algorithm for directly solving the total variational based minimization problems with DD. Various numerical experiments and comparisons demonstrate that the larger the image size is, the more efficient the proposed method is in saving running time. The parallelization has also been realized by using the parallel computing toolbox of MATLAB.

AB - As a fundamental problem in image processing, image deblurring has still attracted a lot of research attention. Due to the large computational cost, especially for high-resolution images, it becomes challenging to solve the deblurring minimization problem and the underlying partial differential equations. The domain decomposition method (DD), as one of the most efficient algorithms for solving large scale problems, had not been applied directly to image deblurring because of the global characteristic of the blur operator. In this paper, in order to avoid separating the blur operator, we propose an algorithm for directly solving the total variational based minimization problems with DD. Various numerical experiments and comparisons demonstrate that the larger the image size is, the more efficient the proposed method is in saving running time. The parallelization has also been realized by using the parallel computing toolbox of MATLAB.

KW - Image deblurring

KW - Overlapping domain decomposition

KW - Total variation minimization

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M3 - Review article

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EP - 414

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Domain decomposition method for image deblurring

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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