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Non-Convex Sparse Regularization Image Restoration via Atan Function.

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Title: Non-Convex Sparse Regularization Image Restoration via Atan Function.
Authors: Zhijun Luo1 ldlzj123@163.com, Zhibin Zhu2 optimization_zhu@163.com, Lirong Wang3 ldwlr1234@163.com, Yingying Li4 yingyli@qq.com
Source: IAENG International Journal of Applied Mathematics. Aug2025, Vol. 55 Issue 8, p2521-2527. 7p.
Subjects: Image reconstruction, Sparse approximations, Mathematical programming, Multipliers (Mathematical analysis), Mathematical functions, Nonconvex programming
Abstract: This study introduces an innovative approach within the sparse regularization framework, replacing the traditional total variation (TV) regularization with a non-convex regularizer based on the arctangent (Atan) function. The Atan-based regularization improves sparse representation and edge preservation through its non-convex properties, effectively overcoming the limitations of convex regularizers in detail reconstruction and artifact suppression. The model ensures overall convexity with careful parameter selection, thus maintaining guaranteed convergence during optimization. The alternating direction method of multipliers (ADMM) algorithm is employed to address the optimization challenges of the non-convex regularizer, demonstrating robust computational efficiency. Extensive experiments on image deblurring tasks show that the proposed method significantly outperforms traditional TV-based approaches in quantitative metrics and visual quality. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Zhijun+Luo%22">Zhijun Luo</searchLink><relatesTo>1</relatesTo><i> ldlzj123@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhibin+Zhu%22">Zhibin Zhu</searchLink><relatesTo>2</relatesTo><i> optimization_zhu@163.com</i><br /><searchLink fieldCode="AR" term="%22Lirong+Wang%22">Lirong Wang</searchLink><relatesTo>3</relatesTo><i> ldwlr1234@163.com</i><br /><searchLink fieldCode="AR" term="%22Yingying+Li%22">Yingying Li</searchLink><relatesTo>4</relatesTo><i> yingyli@qq.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Aug2025, Vol. 55 Issue 8, p2521-2527. 7p.
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  Data: <searchLink fieldCode="DE" term="%22Image+reconstruction%22">Image reconstruction</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+approximations%22">Sparse approximations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br /><searchLink fieldCode="DE" term="%22Multipliers+%28Mathematical+analysis%29%22">Multipliers (Mathematical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Nonconvex+programming%22">Nonconvex programming</searchLink>
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  Data: This study introduces an innovative approach within the sparse regularization framework, replacing the traditional total variation (TV) regularization with a non-convex regularizer based on the arctangent (Atan) function. The Atan-based regularization improves sparse representation and edge preservation through its non-convex properties, effectively overcoming the limitations of convex regularizers in detail reconstruction and artifact suppression. The model ensures overall convexity with careful parameter selection, thus maintaining guaranteed convergence during optimization. The alternating direction method of multipliers (ADMM) algorithm is employed to address the optimization challenges of the non-convex regularizer, demonstrating robust computational efficiency. Extensive experiments on image deblurring tasks show that the proposed method significantly outperforms traditional TV-based approaches in quantitative metrics and visual quality. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      Pagination:
        PageCount: 7
        StartPage: 2521
    Subjects:
      – SubjectFull: Image reconstruction
        Type: general
      – SubjectFull: Sparse approximations
        Type: general
      – SubjectFull: Mathematical programming
        Type: general
      – SubjectFull: Multipliers (Mathematical analysis)
        Type: general
      – SubjectFull: Mathematical functions
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      – SubjectFull: Nonconvex programming
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      – TitleFull: Non-Convex Sparse Regularization Image Restoration via Atan Function.
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            NameFull: Zhijun Luo
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            NameFull: Lirong Wang
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            NameFull: Yingying Li
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            – D: 01
              M: 08
              Text: Aug2025
              Type: published
              Y: 2025
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