From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Denoising
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Inspired by the recent advances of Generative Adversarial Networks (GAN) in deep learning, we propose a novel rank minimization approach, termed rank residual constraint (RRC), for image denoising in the optimization framework. Different from GAN, where a discriminative model is trained jointly with a generative model, in image denoising, since the labels are not available, we build an unsupervised mechanism, where two generative models are employed and jointly optimized. Specifically, by integrating the image nonlocal self-similarity prior with the proposed RRC model, we develop an iterative algorithm for image denoising. We first present a recursive based nonlocal means approach to obtain a good reference of the original image patch groups, and then the rank residual of image patch groups between this reference and the noisy image is minimized to achieve a better estimate of the desired image. In this manner, both the reference and the estimated image in each iteration are improved gradually and jointly; in the meantime, we progressively approximate the underlying low-rank matrix (constructed by image patch groups) via minimizing the rank residual, which is different from existing low-rank based approaches that estimate the underlying low-rank matrix directly from the corrupted observation. We further provide a theoretical analysis on the feasibility of the proposed RRC model from the perspective of group-based sparse representation. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art denoising methods.
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