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From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration
Zhiyuan Zha1; Xin Yuan2; Bihan Wen3; Jiantao Zhou4,5; Jiachao Zhang6; Ce Zhu1
Source PublicationIEEE Transactions on Image Processing

In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observations, we progressively approximate the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, including image denoising and image compression artifacts reduction. Towards this end, we first obtain a good reference of the original image groups by using the image NSS prior, and then the rank residual of the image groups between this reference and the degraded image is minimized to achieve a better estimate to the desired image. In this manner, both the reference and the estimated image are updated gradually and jointly in each iteration. Based on the group-based sparse representation model, we further provide an analytical investigation on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC method outperforms many state-of-the-art schemes in both the objective and perceptual quality.

KeywordLow-rank Rank Residual Constraint Nuclear Norm Minimization Nonlocal Self-similarity Group-based Sparse Representation Image Restoration
URLView the original
Indexed BySCIE
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS IDWOS:000510750900029
Scopus ID2-s2.0-85079574523
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Cited Times [WOS]:13   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorZhiyuan Zha
Affiliation1.School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2.Nokia Bell Labs, Murray Hill, NJ 07974 USA
3.chool of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
4.State Key Laboratory of Internet of Things for Smart City, University of Macau, Macau 999078, China
5.Department of Computer and Information Science, University of Macau, Macau 999078, China
6.Artificial Intelligence Institute of Industrial Technology, Nanjing Institute of Technology, Nanjing 211167, China
Recommended Citation
GB/T 7714
Zhiyuan Zha,Xin Yuan,Bihan Wen,et al. From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration[J]. IEEE Transactions on Image Processing,2019,29:3254-3269.
APA Zhiyuan Zha,Xin Yuan,Bihan Wen,Jiantao Zhou,Jiachao Zhang,&Ce Zhu.(2019).From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration.IEEE Transactions on Image Processing,29,3254-3269.
MLA Zhiyuan Zha,et al."From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration".IEEE Transactions on Image Processing 29(2019):3254-3269.
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