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The Rank Residual Constraint Model with Weighted Schatten p-Norm Minimization for Image Denoising

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Abstract

Low-rank matrix recovery (LRMR) has a wide range of applications in computer vision. In recent years, the rank residual constraint (RRC) model, which aims to approximate the underlying low-rank matrix via minimizing the rank residual, has provided a new idea for LRMR. Different from the RRC model which employs \(l_1\) norm as the regularization term, this paper exploits the weighted Schatten p-norm as the regularizer for the rank residual to obtain a new rank minimization model, namely the rank residual constraint model with adaptive weighted Schatten p-norm (SRRC). The proposed SRRC considers the importance of different rank residual components and gives better approximation to the original low-rank assumption. In the SRRC model, the adaptive p-values can vary with the sparsity of the rank residuals and different weights are assigned to different rank residuals. Thus, the proposed SRRC not only improves the sparsity of the rank residuals but also alleviates the over-penalty of the large singular values. We analyze the solution of SRRC model and prove that its global optimum can be efficiently solved by the generalized soft thresholding algorithm (GST). Extensive experimental results demonstrate that the proposed algorithm achieves favorable performance compared to many popular or state-of-the-art image denoising methods in terms of both objective and visual perception.

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Data Availability Statement

The data that support the findings of this study are openly available on the website https://github.com/zt9877/SRRC.git.

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Acknowledgements

The authors would like to thank editor and anonymous reviewers who gave valuable suggestion that has helped to improve the quality of the paper. Tao Zhang acknowledges the support by the National Natural Science Foundation of China under Grant 61701004, the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province under Grant gxyq2021178 and the Open Fund of Key Laboratory of Anhui Higher Education Institutes under Grant CS2021-07. Xutao Mo acknowledges the support by the University Natural Science Research Project of Anhui Province of China under Grant KJ2020A0238 and the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province under Grant gxyq2022014.

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Authors and Affiliations

  1. School of Mathematics and Physics, Anhui University of Technology, No. 59 Hudong Road, Ma’anshan, 243002, Anhui, China

    Tao Zhang, Di Wu & Xutao Mo

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  1. Tao Zhang
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  2. Di Wu
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Contributions

Conceptualization: [Tao Zhang]; Methodology: [Tao Zhang]; Formal analysis and investigation: [Di Wu]; Writing–original draft preparation: [Di Wu, Tao Zhang]; Writing–review and editing: [Tao Zhang]; Funding acquisition: [Tao Zhang, Xutao Mo]; Resources: [Tao Zhang]; Supervision: [Tao Zhang, Xutao Mo]; Validation: [Di Wu, Xutao Mo]; Visualization:[Di Wu].

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Correspondence to Tao Zhang.

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Zhang, T., Wu, D. & Mo, X. The Rank Residual Constraint Model with Weighted Schatten p-Norm Minimization for Image Denoising. Circuits Syst Signal Process 42, 4740–4758 (2023). https://doi.org/10.1007/s00034-023-02330-5

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