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<p>While the nuclear norm minimization (NNM) has been widely utilized in image processing, its uniform treatment of singular values often leads to excessive rank shrinkage, consequently resulting in suboptimal restoration performance. In this paper, we propose a novel Cauchy noise removal model through the weighted Schatten <i>p</i>-norm minimization (WSNM), which adaptively penalizes singular values to better preserve image structural sparsity. The proposed model is solved via an efficient alternating minimization framework: one subproblem achieves its global optimum efficiently through the Generalized Soft Thresholding (GST) algorithm, while the other is addressed by the Newton method. Numerical experiments demonstrate that the proposed method is more effective than the existing state-of-the-art methods in removing Cauchy noise, both in terms of visual quality and quantitative assessment.</p>

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Cauchy Noise Removal Based on Weighted Schatten p-Norm Minimization

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Jianguang Zhu,
  • Wen Gao,
  • Binbin Hao

摘要

While the nuclear norm minimization (NNM) has been widely utilized in image processing, its uniform treatment of singular values often leads to excessive rank shrinkage, consequently resulting in suboptimal restoration performance. In this paper, we propose a novel Cauchy noise removal model through the weighted Schatten p-norm minimization (WSNM), which adaptively penalizes singular values to better preserve image structural sparsity. The proposed model is solved via an efficient alternating minimization framework: one subproblem achieves its global optimum efficiently through the Generalized Soft Thresholding (GST) algorithm, while the other is addressed by the Newton method. Numerical experiments demonstrate that the proposed method is more effective than the existing state-of-the-art methods in removing Cauchy noise, both in terms of visual quality and quantitative assessment.