Low-Rank and Sparse Matrix Recovery for Hyperspectral Image Reconstruction Using Bayesian Learning
- The proposed method gives the structure of the covariance matrix of the L&S signals, models HSI data with the L&S structure, and utilizes the CS and Bayesian learning methods to compress and reconstruct HSI data.
- In the reconstruction part, the proposed method makes use of the relationship between multiple dimensions of high-dimensional data and combines data reconstruction with HSI data acquisition. It can be used to realize the segmented acquisition, compression, and transmission of HSI data so as to reduce the amount of calculation and data transmission that must be performed in the satellite.
- We demonstrate the superior performance of the proposed method in comparison with state-of-the-art alternatives by conducting experiments on both synthetic signals and real signals.
2. Two-Dimensional Reconstruction Methods for HSI Data
- Estimation of .After the Bayesian posterior probability is obtained with the Bayesian rule, the maximum a posteriori (MAP) is used to obtain the estimation of :
- Estimation of .In order to obtain , we simplify the expression of asAfter maximizing the logarithm of the joint probability of and , we take the derivative of it with respect to :
- Estimation of .
- Estimation of .The algorithm calculates the singular values of through singular value decomposition (SVD) for each slice of the HSI data and sorts the singular values in descending order. Depending on the singular value of the sequence, we can obtain the value of the corresponding , . The corresponding to the larger singular value is 1, or is otherwise 0. For HSI data, a large singular value distribution can be obtained by analyzing only one segment of its 2D slice signal in advance. The expression of is
- Estimation of .
2.1. Two-Dimensional HSI Reconstruction Algorithm—L&S-bSBL (1)
- According to the different bands M, we use the tensor to expand with , , ;
- let , turn into , by using the operator;
- let , ;
- obtain the corresponding value of in the DCT domain .
2.2. Two-Dimensional HSI Reconstruction Algorithm—L&S-bSBL (2)
- Let slices and , as ;
- obtain the corresponding value of in the DCT domain , , ;
- let turn into , , by using the vec operator.
3. L&S Reconstruction Algorithm Combined with Acquisition Methods
3.1. Problem Formulation and Signal Model
3.2. Proposed Method
|Algorithm 1 Proposed method|
3.3. Simulation Experiments
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
- Chang, C.I. Hyperspectral Data Exploitation: Theory and Applications; John Wiley & Sons: Hoboken, NJ, USA, 2007. [Google Scholar]
- Bioucas-Dias, J.M.; Plaza, A.; Camps-Valls, G.; Scheunders, P.; Nasrabadi, N.; Chanussot, J. Hyperspectral remote sensing data analysis and future challenges. IEEE Geosci. Remote Sens. Mag. 2013, 1, 6–36. [Google Scholar] [CrossRef][Green Version]
- Goetz, A.F. Three decades of hyperspectral remote sensing of the Earth: A personal view. Remote Sens. Environ. 2009, 113, S5–S16. [Google Scholar] [CrossRef]
- Borengasser, M.; Hungate, W.S.; Watkins, R. Hyperspectral Remote Sensing: Principles and Applications, 1st ed.; CRC Press: Boca Raton, FL, USA, 2007. [Google Scholar]
- Zhang, H.; He, W.; Zhang, L.; Shen, H.; Yuan, Q. Hyperspectral image restoration using low-rank matrix recovery. IEEE Trans. Geosci. Remote Sens. 2014, 52, 4729–4743. [Google Scholar] [CrossRef]
- Golbabaee, M.; Vandergheynst, P. Hyperspectral image compressed sensing via low-rank and joint-sparse matrix recovery. In Proceedings of the 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Kyoto, Japan, 25–30 March 2012; pp. 2741–2744. [Google Scholar]
- Li, C.; Ma, L.; Wang, Q.; Zhou, Y.; Wang, N. Construction of sparse basis by dictionary training for compressive sensing hyperspectral imaging. In Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium—IGARSS, Melbourne, Australia, 21–26 July 2013; pp. 1442–1445. [Google Scholar]
- Hou, Y.; Zhang, Y. Effective hyperspectral image block compressed sensing using thress-dimensional wavelet transform. In Proceedings of the 2014 IEEE Geoscience and Remote Sensing Symposium, Quebec, QC, Canada, 13–18 July 2014; pp. 2973–2976. [Google Scholar]
- Donoho, D. Compressed sensing. IEEE Trans. Inf. Theory 2006, 52, 1289–1306. [Google Scholar] [CrossRef]
- Baraniuk, R.G. Compressive Sensing [Lecture Notes]. IEEE Signal Process. Mag. 2007, 24, 118–121. [Google Scholar] [CrossRef]
- Candes, E.J.; Wakin, M.B. An Introduction To Compressive Sampling. IEEE Signal Process. Mag. 2008, 25, 21–30. [Google Scholar] [CrossRef]
- Zhang, Y.; Li, Y.; Yin, C.; He, K. Low-rank and joint-sparse signal recovery for spatially and temporally correlated data using sparse Bayesian learning. In Proceedings of the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada, 15–20 April 2018; pp. 4719–4723. [Google Scholar]
- Wang, L.; Feng, Y.; Gao, Y.; Wang, Z.; He, M. Compressed Sensing Reconstruction of Hyperspectral Images Based on Spectral Unmixing. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2018, 11, 1266–1284. [Google Scholar] [CrossRef]
- Wang, Z.; Xiao, H.; He, M.; Wang, L.; Xu, K.; Nian, Y. Spatial-Spectral Joint Compressed Sensing for Hyperspectral Images. IEEE Access 2020, 8, 149661–149675. [Google Scholar] [CrossRef]
- Xiao, H.; Wang, Z.; Cui, X. Distributed Compressed Sensing of Hyperspectral Images According to Spectral Library Matching. IEEE Access 2021, 9, 112994–113006. [Google Scholar] [CrossRef]
- Yang, S.; Wang, M.; Li, P.; Jin, L.; Wu, B.; Jiao, L. Compressive Hyperspectral Imaging via Sparse Tensor and Nonlinear Compressed Sensing. IEEE Trans. Geosci. Remote Sens. 2015, 53, 5943–5957. [Google Scholar] [CrossRef]
- He, W.; Zhang, H.; Shen, H.; Zhang, L. Hyperspectral Image Denoising Using Local Low-Rank Matrix Recovery and Global Spatial–Spectral Total Variation. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2018, 11, 713–729. [Google Scholar] [CrossRef]
- Takeyama, S.; Ono, S. Joint Mixed-Noise Removal and Compressed Sensing Reconstruction of Hyperspectral Images via Convex Optimization. In Proceedings of the IGARSS 2020—2020 IEEE International Geoscience and Remote Sensing Symposium, Waikoloa, HI, USA, 26 September–2 October 2020; pp. 1492–1495. [Google Scholar]
- Fu, W.; Li, S. Semi-Tensor Compressed Sensing for Hyperspectral Image. In Proceedings of the IGARSS 2018—2018 IEEE International Geoscience and Remote Sensing Symposium, Valencia, Spain, 22–27 July 2018; pp. 2737–2740. [Google Scholar]
- Zhang, Y.; Huang, L.; Li, Y.; Zhang, K.; Yin, C. Fast recovery of low-rank and joint-sparse signals in wireless body area networks. In Proceedings of the 2020 IEEE/CIC International Conference on Communications in China (ICCC), Chongqing, China, 9–11 August 2020; pp. 577–581. [Google Scholar]
- Xin, B.; Wang, Y.; Gao, W.; Wipf, D. Exploring algorithmic limits of matrix rank minimization under affine constraints. IEEE Trans. Signal Process. 2016, 64, 4960–4974. [Google Scholar] [CrossRef]
- Chen, W. Simultaneously sparse and low-rank matrix reconstruction via nonconvex and nonseparable regularization. IEEE Trans. Signal Process. 2018, 66, 5313–5323. [Google Scholar] [CrossRef]
- Li, Y.; Chen, W.; Yin, C.; Han, Z. Approximate message passing for sparse recovering of spatially and temporally correlated data. In Proceedings of the 2015 IEEE/CIC International Conference on Communications in China (ICCC), Shenzhen, China, 2–4 November 2015; pp. 1–6. [Google Scholar]
- Ziniel, J.; Schniter, P. Efficient high-dimensional inference in the multiple measurement vector problem. IEEE Trans. Signal Process. 2013, 61, 340–354. [Google Scholar] [CrossRef]
- Zhang, Z.; Jung, T.P.; Makeig, S.; Rao, B.D. Compressed sensing of EEG for wireless telemonitoring with low energy consumption and inexpensive hardware. IEEE Trans. Biomed. Eng. 2013, 60, 221–224. [Google Scholar] [CrossRef] [PubMed][Green Version]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Zhang, Y.; Huang, L.-T.; Li, Y.; Zhang, K.; Yin, C. Low-Rank and Sparse Matrix Recovery for Hyperspectral Image Reconstruction Using Bayesian Learning. Sensors 2022, 22, 343. https://doi.org/10.3390/s22010343
Zhang Y, Huang L-T, Li Y, Zhang K, Yin C. Low-Rank and Sparse Matrix Recovery for Hyperspectral Image Reconstruction Using Bayesian Learning. Sensors. 2022; 22(1):343. https://doi.org/10.3390/s22010343Chicago/Turabian Style
Zhang, Yanbin, Long-Ting Huang, Yangqing Li, Kai Zhang, and Changchuan Yin. 2022. "Low-Rank and Sparse Matrix Recovery for Hyperspectral Image Reconstruction Using Bayesian Learning" Sensors 22, no. 1: 343. https://doi.org/10.3390/s22010343