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Image denoising via double-weighted correlated total variation regularization

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Abstract

Image denoising is a widely concerned problem, which has been successfully applied in remote sensing, medicine and other fields. A typical idea of image denoising is to exploit some prior information existing in real-world data, such as low-rank prior and local smoothness prior. Some researchers devote themselves to combining both priors, however, the current methods cannot capture both properties simultaneously and adequately. Motivated by a new regularizer named three-dimensional correlated total variation (3DCTV) for robust principal component analysis problem, in this paper, we propose a new image denoising model via the double-weighted correlated total variation regularization. Specifically, we perform weighting operations on the 3DCTV regularization term and the sparse term separately, which can make fuller use of the low-rank prior, the local smoothness prior and the sparse prior of images. In addition, we add the Frobenius norm term to this model for modeling strong Gaussian noise in some real-world scenarios. Then, we develop an efficient algorithm to solve the resulting optimization problem by using the well-known alternating direction method of multipliers. Finally, we conduct extensive experiments on hyperspectral images, multispectral images and medical images under various noise situations, and the experimental results show that the proposed method outperforms the existing state-of-the-art denoising methods. Especially when the test image is polluted by low-intensity sparse noise, the MPSNR index of our method is about 5 points higher than that of the 3DCTV method.

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Availability of data and materials

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported in part by the National Natural Science Foundation of China’s Regional Innovation Development Joint Fund under Grant U24A2001; in part by the Natural Science Foundation of Chongqing, China, under Grant CSTB2023NSCQ-LZX0044; in part by the National Natural Science Foundation of China under Grant 12071380, Grant 12301594, Grant 12201505, Grant 12101512; and in part by the Chongqing Talent Project, China, under Grant cstc2021ycjh-bgzxm0015.

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Zhihao Zhang: Conceptualization, Methodology, Software, Writing - Original Draft; Peng Zhang: Data Curation; Xinling Liu: Writing - Reviewing and Editing, Formal analysis; Jingyao Hou: Visualization, Investigation; Qingrong Feng: Software, Validation; Jianjun Wang: Supervision, Project administration.

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Correspondence to Jianjun Wang.

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Zhang, Z., Zhang, P., Liu, X. et al. Image denoising via double-weighted correlated total variation regularization. Appl Intell 55, 269 (2025). https://doi.org/10.1007/s10489-024-06024-6

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