Two-Stage Image Denoising via an Enhanced Low-Rank Prior

Restoring the image contaminated with heavy noise remains a challenging task. Since the image prior is essential to restoring a high-quality image, this paper proposes a novel two-stage enhanced low-rank prior model (TSLR) for efficient image denoising. Unlike denoising an image as a whole, this algorithm divides the denoising process into two stages: contour restoration and detail restoration. First, we explore the total variation (TV) regularization term to restore the image contour, obtaining the preliminary denoised image. Although TV regularization term can reduce noise, it loses the rich details of the original image. Nevertheless, detail preservation ensures good visual quality of the denoised images. Then, to overcome the above issue, the preliminary denoised image is adopted as a rough evaluation of the original image for the second stage, and the weighted sum of the L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document}-norm and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}-norm is utilized as the fidelity term. Furthermore, we introduce a new enhanced low-rank prior, which combines the low-rank prior of similar patches from both gray and gradient domains, to reconstruct the fine details of the image. To further improve the validity of image denoising on the basis of the low-rank prior, the weighted nuclear norm minimization method is adopted in the present study. In addition, this work adaptively selects the search window size for different regions to accurately select similar patches. Through extensive experiments, the results reveal that our scheme can retain more detailed information while eliminating noise and can surpass a variety of advanced non-deep methods regarding both the PSNR and SSIM.