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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 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 a theoretical analysis on the
feasibility of the proposed RRC model. Experimental results demonstrate that
the proposed RRC model outperforms many state-of-the-art schemes in both the
objective and perceptual quality
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