All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral Denoising
Hyperspectral image (HSI) processing tasks frequently rely on spatial–spectral total variation (SSTV) to quantify the local smoothness of image structures. However, conventional SSTV only considers a sparse structure of gradient maps computed along the spatial and spectral dimensions whil...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10201900/ |
| _version_ | 1797743480295915520 |
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| author | Haijin Zeng Shaoguang Huang Yongyong Chen Hiep Luong Wilfried Philips |
| author_facet | Haijin Zeng Shaoguang Huang Yongyong Chen Hiep Luong Wilfried Philips |
| author_sort | Haijin Zeng |
| collection | DOAJ |
| description | Hyperspectral image (HSI) processing tasks frequently rely on spatial–spectral total variation (SSTV) to quantify the local smoothness of image structures. However, conventional SSTV only considers a sparse structure of gradient maps computed along the spatial and spectral dimensions while neglecting other correlations. To address this limitation, we introduce low-rank guided SSTV (LRSTV), which characterizes the sparsity and low-rank priors of the gradient map simultaneously. First, we verify through numerical tests and theoretical analyses that the gradient tensors are not only sparse but also low-rank. Subsequently, to model the low rankness of the gradient map, we use the tensor average rank to represent the low Tucker rank of gradient tensors. The convex envelope of the tensor average rank is then employed to penalize the rank on the gradient map after the Fourier transform along the spectral dimension. By naturally encoding the sparsity and low-rank priors of the gradient map, LRSTV results in a more accurate representation of the original image. Finally, we demonstrate the effectiveness of LRSTV by integrating it into the HSI processing model, replacing conventional SSTV, and testing it on two public datasets with nine cases of mixed noise and two datasets with realistic noise. The results show that LRSTV outperforms conventional SSTV in terms of accuracy and robustness. |
| first_indexed | 2024-03-12T14:56:01Z |
| format | Article |
| id | doaj.art-d7fe84226e4e4929abb85a3eaa880c5f |
| institution | Directory Open Access Journal |
| issn | 2151-1535 |
| language | English |
| last_indexed | 2024-03-12T14:56:01Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| spelling | doaj.art-d7fe84226e4e4929abb85a3eaa880c5f2023-08-14T23:00:15ZengIEEEIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing2151-15352023-01-01167357737310.1109/JSTARS.2023.330114910201900All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral DenoisingHaijin Zeng0https://orcid.org/0000-0003-0398-3316Shaoguang Huang1https://orcid.org/0000-0001-5439-5018Yongyong Chen2https://orcid.org/0000-0003-1970-1993Hiep Luong3https://orcid.org/0000-0002-6246-5538Wilfried Philips4https://orcid.org/0000-0003-4456-4353Image Processing and Interpretation, imec Research Group, Ghent University, Gent, BelgiumSchool of Computer Science, China University of Geosciences, Wuhan, ChinaSchool of Computer Science and Technology, Harbin Institute of Technology Shenzhen, Shenzhen, ChinaImage Processing and Interpretation, imec Research Group, Ghent University, Gent, BelgiumImage Processing and Interpretation, imec Research Group, Ghent University, Gent, BelgiumHyperspectral image (HSI) processing tasks frequently rely on spatial–spectral total variation (SSTV) to quantify the local smoothness of image structures. However, conventional SSTV only considers a sparse structure of gradient maps computed along the spatial and spectral dimensions while neglecting other correlations. To address this limitation, we introduce low-rank guided SSTV (LRSTV), which characterizes the sparsity and low-rank priors of the gradient map simultaneously. First, we verify through numerical tests and theoretical analyses that the gradient tensors are not only sparse but also low-rank. Subsequently, to model the low rankness of the gradient map, we use the tensor average rank to represent the low Tucker rank of gradient tensors. The convex envelope of the tensor average rank is then employed to penalize the rank on the gradient map after the Fourier transform along the spectral dimension. By naturally encoding the sparsity and low-rank priors of the gradient map, LRSTV results in a more accurate representation of the original image. Finally, we demonstrate the effectiveness of LRSTV by integrating it into the HSI processing model, replacing conventional SSTV, and testing it on two public datasets with nine cases of mixed noise and two datasets with realistic noise. The results show that LRSTV outperforms conventional SSTV in terms of accuracy and robustness.https://ieeexplore.ieee.org/document/10201900/Hyperspectral images (HSIs)restorationspatial–spectraltotal variation (TV) |
| spellingShingle | Haijin Zeng Shaoguang Huang Yongyong Chen Hiep Luong Wilfried Philips All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral Denoising IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Hyperspectral images (HSIs) restoration spatial–spectral total variation (TV) |
| title | All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral Denoising |
| title_full | All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral Denoising |
| title_fullStr | All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral Denoising |
| title_full_unstemmed | All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral Denoising |
| title_short | All of Low-Rank and Sparse: A Recast Total Variation Approach to Hyperspectral Denoising |
| title_sort | all of low rank and sparse a recast total variation approach to hyperspectral denoising |
| topic | Hyperspectral images (HSIs) restoration spatial–spectral total variation (TV) |
| url | https://ieeexplore.ieee.org/document/10201900/ |
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