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<p>A new variational model for removing impulse noise is proposed in this paper. In the new model, we combine high-order total variation prior with nuclear norm regularization to better preserve the image edge and eliminate the staircase effect. Meanwhile, we use <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\ell _0\)</EquationSource> </InlineEquation> data fidelity term to effectively detect and remove impulse noise. Numerically, by integrating soft threshold operator, singular value decomposition and Semi-implicit gradient projection algorithm, we propose a modified alternating direction method of multipliers to solve the proposed model. In addition, the convergence analysis for the proposed method is established. Experimental results show that our proposed model outperforms some existing state-of-the-art image restoration methods in terms of visual quality and quantitative evaluation metrics.</p>

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Impulse noise image restoration using \(\ell _0\)-norm fidelity model and hybrid regularizers

  • 期刊论文

  • 发表日期：

    2025年10月16日

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  • Jianguang Zhu,
  • Jing Pan,
  • Zhanglin Bo,
  • Binbin Hao

摘要

A new variational model for removing impulse noise is proposed in this paper. In the new model, we combine high-order total variation prior with nuclear norm regularization to better preserve the image edge and eliminate the staircase effect. Meanwhile, we use \(\ell _0\) data fidelity term to effectively detect and remove impulse noise. Numerically, by integrating soft threshold operator, singular value decomposition and Semi-implicit gradient projection algorithm, we propose a modified alternating direction method of multipliers to solve the proposed model. In addition, the convergence analysis for the proposed method is established. Experimental results show that our proposed model outperforms some existing state-of-the-art image restoration methods in terms of visual quality and quantitative evaluation metrics.