An iterative decoupled method with weighted nuclear norm minimization for image restoration

ABSTRACT

Recently, iterative methods based on decoupling of deblurring and denoising steps have received remarkable attention in image processing problems. In this paper, we propose an effective iterative decoupled approach for image restoration. The main idea is to split the image restoration problem into two minimization subproblems: deblurring and denoising. An efficient deblurring method using fast transforms is used in the deblurring step and a weighted nuclear norm minimization method is employed in the denoising step. We analyze the convergence of the developed iterative method under some assumptions. Some numerical experiments are given to demonstrate the effectiveness of the proposed method.

KEYWORDS:

• Image restoration
• weighted nuclear norm
• decoupled method
• regularization
• noise

AMS SUBJECT CLASSIFICATIONS:

• 68U10
• 15A29
• 65K05

Acknowledgements

The authors would like to express their great thankfulness to the referees for much constructive, detailed and helpful advice regarding revising this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSFC - National Natural Science Foundation of China (11671002, 61731009), Nature Science Foundation of Jiangsu Province (BK20181483), Science and Technology Commission of Shanghai Municipality (18dz2271000), Jiangsu Key Lab for NSLSCS (201806), Qing Lan Project and Hai Yan project, Lianyungang 521 project and NSF of HHIT (Z2017004).