Image Denoising with Adaptive Weighted Graph Filtering |
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Authors: | Ying Chen Yibin Tang Lin Zhou Yan Zhou Jinxiu Zhu Li Zhao |
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Affiliation: | 1.School of Information Science and Engineering, Southeast University, Nanjing, 210096, China.
2 Department of Psychiatry and Translational Imaging, Columbia University & NYSPI, New York, 10032, USA. 3 College of Internet of Things Engineering, Hohai University, Changzhou, 213022, China.
4 Changzhou Key Laboratory of Sensor Networks and Environmental Sensing, Changzhou, 213022, China. |
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Abstract: | Graph filtering, which is founded on the theory of graph signal processing, is
proved as a useful tool for image denoising. Most graph filtering methods focus on learning
an ideal lowpass filter to remove noise, where clean images are restored from noisy ones by
retaining the image components in low graph frequency bands. However, this lowpass filter
has limited ability to separate the low-frequency noise from clean images such that it makes
the denoising procedure less effective. To address this issue, we propose an adaptive
weighted graph filtering (AWGF) method to replace the design of traditional ideal lowpass
filter. In detail, we reassess the existing low-rank denoising method with adaptive
regularizer learning (ARLLR) from the view of graph filtering. A shrinkage approach
subsequently is presented on the graph frequency domain, where the components of noisy
image are adaptively decreased in each band by calculating their component significances.
As a result, it makes the proposed graph filtering more explainable and suitable for
denoising. Meanwhile, we demonstrate a graph filter under the constraint of subspace
representation is employed in the ARLLR method. Therefore, ARLLR can be treated as a
special form of graph filtering. It not only enriches the theory of graph filtering, but also
builds a bridge from the low-rank methods to the graph filtering methods. In the
experiments, we perform the AWGF method with a graph filter generated by the classical
graph Laplacian matrix. The results show our method can achieve a comparable denoising
performance with several state-of-the-art denoising methods. |
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Keywords: | Graph filtering image denoising Laplacian matrix low rank |
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