From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

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 un...

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Bibliographic Details
Published in:IEEE transactions on image processing 2020-01, Vol.29, p.3254-3269
Main Authors: Zha, Zhiyuan, Yuan, Xin, Wen, Bihan, Zhou, Jiantao, Zhang, Jiachao, Zhu, Ce
Format: Article
Language:English
Subjects:
Analytical models
Constraint modelling
Estimation
group-based sparse representation
Image compression
Image degradation
Image denoising
Image reconstruction
Image restoration
Iterative methods
Low-rank
Minimization
Noise reduction
nonlocal self-similarity
nuclear norm minimization
Optimization
rank residual constraint
Self-similarity
Sparse matrices
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Summary: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.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2019.2958309