Year: 2025
Author: Wenli Yang, Zhongyi Huang, Wei Zhu
CSIAM Transactions on Applied Mathematics, Vol. 6 (2025), Iss. 2 : pp. 380–411
Abstract
We propose a novel two-stage model for image denoising. With the group sparse representations over local singular value decomposition stage (locally), one can remove the noise effectively and keep the texture well. The final denoising by a first-order variational model stage (globally) can help us to remove artifacts, maintain the image contrast, suppress the staircase effect, while preserving sharp edges. The existence and uniqueness of global minimizers of the low-rank problem based on group sparse representations are analyzed and proved. Alternating direction method of multipliers is utilized to minimize the associated functional, and the convergence analysis of the proposed optimization algorithm are established. Numerical experiments are conducted to showcase the distinctive features of our method and to provide a comparison with other image denoising techniques.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2024-0030
CSIAM Transactions on Applied Mathematics, Vol. 6 (2025), Iss. 2 : pp. 380–411
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Image denoising variational model group sparse representations.