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Volume 22, Issue 1
Image Smoothing via a Novel Adaptive Weighted $L_0$ Regularization

Wufan Zhao, Tingting Wu, Chenchen Feng, Wenna Wu, Xiaoguang Lv, Hongming Chen & Jun Liu

DOI: 10.4208/ijnam2025-1002

Int. J. Numer. Anal. Mod., 22 (2025), pp. 21-39.

Published online: 2024-11

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  • Abstract

Image smoothing has been extensively used in various fields, e.g., edge extraction, image abstraction, and image detail enhancement. Many existing optimization-based image smoothing methods have been proposed in recent years. The downside of these methods is that the results often have unclear edges and missing structures. To obtain satisfactory smoothing results, we design a novel optimization model by introducing an anisotropic $L_0$ gradient intensity. Specifically, a weighted matrix $T$ is imposed to control further the sparsity of the gradient measured by $L_0$-norm. Since the proposed model is non-convex and non-smooth, we apply the half quadratic splitting (HQS) algorithm to solve it effectively. In addition, to obtain a more suitable regularization parameter $λ,$ we utilize an adaptive parameter selection method based on Morozovs discrepancy principle. Finally, we conduct numerical experiments to illustrate the superiority of our method over some state-of-the-art methods.

  • Keywords

Image smoothing, adaptive weighted matrix, $L_0$ gradient minimization, parameter selection.

  • AMS Subject Headings

65D18, 68U10, 94A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-22-21, author = {Zhao , WufanWu , TingtingFeng , ChenchenWu , WennaLv , XiaoguangChen , Hongming and Liu , Jun}, title = {Image Smoothing via a Novel Adaptive Weighted $L_0$ Regularization}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {22}, number = {1}, pages = {21--39}, abstract = {

Image smoothing has been extensively used in various fields, e.g., edge extraction, image abstraction, and image detail enhancement. Many existing optimization-based image smoothing methods have been proposed in recent years. The downside of these methods is that the results often have unclear edges and missing structures. To obtain satisfactory smoothing results, we design a novel optimization model by introducing an anisotropic $L_0$ gradient intensity. Specifically, a weighted matrix $T$ is imposed to control further the sparsity of the gradient measured by $L_0$-norm. Since the proposed model is non-convex and non-smooth, we apply the half quadratic splitting (HQS) algorithm to solve it effectively. In addition, to obtain a more suitable regularization parameter $λ,$ we utilize an adaptive parameter selection method based on Morozovs discrepancy principle. Finally, we conduct numerical experiments to illustrate the superiority of our method over some state-of-the-art methods.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1002}, url = {http://global-sci.org/intro/article_detail/ijnam/23565.html} }
TY - JOUR T1 - Image Smoothing via a Novel Adaptive Weighted $L_0$ Regularization AU - Zhao , Wufan AU - Wu , Tingting AU - Feng , Chenchen AU - Wu , Wenna AU - Lv , Xiaoguang AU - Chen , Hongming AU - Liu , Jun JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 21 EP - 39 PY - 2024 DA - 2024/11 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1002 UR - https://global-sci.org/intro/article_detail/ijnam/23565.html KW - Image smoothing, adaptive weighted matrix, $L_0$ gradient minimization, parameter selection. AB -

Image smoothing has been extensively used in various fields, e.g., edge extraction, image abstraction, and image detail enhancement. Many existing optimization-based image smoothing methods have been proposed in recent years. The downside of these methods is that the results often have unclear edges and missing structures. To obtain satisfactory smoothing results, we design a novel optimization model by introducing an anisotropic $L_0$ gradient intensity. Specifically, a weighted matrix $T$ is imposed to control further the sparsity of the gradient measured by $L_0$-norm. Since the proposed model is non-convex and non-smooth, we apply the half quadratic splitting (HQS) algorithm to solve it effectively. In addition, to obtain a more suitable regularization parameter $λ,$ we utilize an adaptive parameter selection method based on Morozovs discrepancy principle. Finally, we conduct numerical experiments to illustrate the superiority of our method over some state-of-the-art methods.

Zhao , WufanWu , TingtingFeng , ChenchenWu , WennaLv , XiaoguangChen , Hongming and Liu , Jun. (2024). Image Smoothing via a Novel Adaptive Weighted $L_0$ Regularization. International Journal of Numerical Analysis and Modeling. 22 (1). 21-39. doi:10.4208/ijnam2025-1002
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