Non-Convex Sparse Regularization Image Restoration via Atan Function.

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Bibliographic Details
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]
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Database:	Engineering Source

Description
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]
ISSN:	19929978