Research Article
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HYPERSPECTRAL ANOMALY DETECTION WITH AN IMPROVED APPROACH: INTEGRATION OF GO DECOMPOSITION ALGORITHM AND LAPLACIAN MATRIX MODIFIER

Year 2024, Issue: 056, 36 - 44, 31.03.2024

Fatma Küçük

https://doi.org/10.59313/jsr-a.1324375

Abstract

In this study, a hyperspectral anomaly detection method based on Laplacian matrix (HADLAP) is proposed. This paper addresses the problem of determining covariance matrix inversion in high-dimensional data and proposes a new approach for identifying anomalies in hyperspectral images (HSIs). The study’s goals are to find anomalous locations in HSIs and to deal with the problem of calculating the inversion of the covariance matrix of high dimensional data. The method is centered on two main concepts. One of them is decomposition process. The other one is detection process. First, HSI data is decomposed as a low rank and sparse matrices. Second, the sparse component of the data is used to build Mahalanobis Distance (MD). In this study, go decomposition (GoDec) algorithm is employed to decompose the data. Then, the distance is calculated by obtained matrix with aim of detection of anomalous pixels in the HSIs. The method differs from previous studies that covariance matrix in the distance is computed with Laplacian matrix and MD. Experiments conducted on three hyperspectral datasets present the superiority and effectiveness of the proposed framework in terms of detection performance with respect to state-of-the-art methods.

Keywords

Anomaly Detection Low-Rank Matrix Laplacian Matrix

References

  • [1] C. I. Chang, Hyperspectral data processing: algorithm design and analysis. Maryland, USA: Wiley, 2013.
  • [2] C. I. Chang, Hyperspectral Imaging: Techniques for Spectral Detection and Classification. Maryland, USA: Springer, 2003.
  • [3] W. Li, G. Wu, and Q. Du, "Transferred deep learning for anomaly detection in hyperspectral imagery,” IEEE Geosci. Remote Sens. Lett., vol. 14, no. 5, pp. 597-601, May 2017, doi: 10.1109/LGRS.2017.2657818.
  • [4] I. S. Reed and X. Yu, "Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution,” IEEE Trans. Acoust. Speech Signal Process., vol. 38, no. 10, pp. 1760-1770, 1990, doi: 10.1109/29.60107.
  • [5] D. W. J. Stein et al., "Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag., vol. 19, no. 1, pp. 58-69, Jan. 2002, doi: 10.1109/79.974730.
  • [6] A. P. Schaum, "Hyperspectral anomaly detection beyond RX,” Proc. SPIE, vol. 6565, pp. 13-25, May 2007, doi: 10.1117/12.718789.
  • [7] T. C. M. Rao, G. J. Sankar, and T. R. Kumar, "A hierarchical hybrid SVM method for classification of remotely sensed data,” J Indian Soc Remote Sens, vol. 40, pp. 191–200, June 2012, doi: 10.1007/s12524-011-0149-4.
  • [8] L. Wan et al., "Collaborative active and semisupervised learning for hyperspectral remote sensing image classification,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 5, pp. 2384-2396, Nov. 2014, doi: 10.1109/TGRS.2014.2359933.
  • [9] H. Su et al., "Hyperspectral anomaly detection: A survey,” IEEE Geosci. Remote Sens. Mag., vol. 10, pp. 64-90, Sept. 2021, doi: 10.1109/MGRS.2021.3105440.
  • [10] Y. Xu et al., "Anomaly detection in hyperspectral images based on low-rank and sparse representation,” IEEE Trans. Geosci. Remote Sens., vol. 54(4), pp. 1990-2000, Nov. 2015, doi: 10.1109/TGRS.2015.2493201
  • [11] W. Xie et al., "Spectral adversarial feature learning for anomaly detection in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens., vol. 58(4), pp. 2352-2365, Nov. 2019, doi: 10.1109/TGRS.2019.2948177.
  • [12] T. Zhou and D. Tao, "Godec: Randomized low-rank & sparse matrix decomposition in noisy case,” Proc. 28th Int. Conf. Machine Learn. (ICML), 2011, pp. 33-40.
  • [13] W. Sun et al., "Low-rank and sparse matrix decomposition-based anomaly detection for hyperspectral imagery,” J. Appl. Remote Sens., vol. 8, no. 1, pp. 083641, 2014, doi: 10.1117/1.JRS.8.083641
  • [14] G. Lerman and T. Maunu, "An overview of robust subspace recovery,” Proc. of IEEE, vol. 106(8), pp. 1380-1410, Aug. 2018, doi: 10.1109/JPROC.2018.2853141
  • [15] F. Küçük, B. Töreyin and F. V. Çelebi, "Sparse and low-rank matrix decomposition-based method for hyperspectral anomaly detection," J. Appl. Remote Sens., vol. 13, no. 1, pp. 014519, Feb. 2019, doi: 10.1117/1.JRS.13.014519.
  • [16] F. Küçük, B. U. Töreyin, F. V. Çelebi, "Anomaly detection in hyperspectral data with matrix decomposition," in: 26th Signal Processing and Communications Applications Conference, SIU, 2018, pp. 1–4, doi: 10.1109/SIU.2018.8404658.
  • [17] F. Küçük, "Hybrid anomaly detection method for hyperspectral images," Signal Image Video Process., vol. 17, pp. 2755-2761, Jan. 2023, doi: 10.1007/s11760-023-02492-4.
  • [18] F. Verdoja and M. Grangetto, "Graph Laplacian for image anomaly detection," Mach. Vis. Appl., vol. 31, no. 1–2, Jan. 2020, doi: 10.1007/s00138-020-01059-4.
  • [19] F. Zhang, F. He, and H. Hu, "Laplacian matrix graph for anomaly target detection in hyperspectral images," Elec. Lett., vol. 58(8), pp. 312-314, Feb. 2022, doi: 10.1049/ell2.12449.
  • [20] L. J. Grady and J. R. Polimeni, Discrete Calculus: Applied Analysis on Graphs for Computational Science. London, UK, Springer, 2010.

Year 2024, Issue: 056, 36 - 44, 31.03.2024

Fatma Küçük

https://doi.org/10.59313/jsr-a.1324375

Abstract

References

  • [1] C. I. Chang, Hyperspectral data processing: algorithm design and analysis. Maryland, USA: Wiley, 2013.
  • [2] C. I. Chang, Hyperspectral Imaging: Techniques for Spectral Detection and Classification. Maryland, USA: Springer, 2003.
  • [3] W. Li, G. Wu, and Q. Du, "Transferred deep learning for anomaly detection in hyperspectral imagery,” IEEE Geosci. Remote Sens. Lett., vol. 14, no. 5, pp. 597-601, May 2017, doi: 10.1109/LGRS.2017.2657818.
  • [4] I. S. Reed and X. Yu, "Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution,” IEEE Trans. Acoust. Speech Signal Process., vol. 38, no. 10, pp. 1760-1770, 1990, doi: 10.1109/29.60107.
  • [5] D. W. J. Stein et al., "Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag., vol. 19, no. 1, pp. 58-69, Jan. 2002, doi: 10.1109/79.974730.
  • [6] A. P. Schaum, "Hyperspectral anomaly detection beyond RX,” Proc. SPIE, vol. 6565, pp. 13-25, May 2007, doi: 10.1117/12.718789.
  • [7] T. C. M. Rao, G. J. Sankar, and T. R. Kumar, "A hierarchical hybrid SVM method for classification of remotely sensed data,” J Indian Soc Remote Sens, vol. 40, pp. 191–200, June 2012, doi: 10.1007/s12524-011-0149-4.
  • [8] L. Wan et al., "Collaborative active and semisupervised learning for hyperspectral remote sensing image classification,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 5, pp. 2384-2396, Nov. 2014, doi: 10.1109/TGRS.2014.2359933.
  • [9] H. Su et al., "Hyperspectral anomaly detection: A survey,” IEEE Geosci. Remote Sens. Mag., vol. 10, pp. 64-90, Sept. 2021, doi: 10.1109/MGRS.2021.3105440.
  • [10] Y. Xu et al., "Anomaly detection in hyperspectral images based on low-rank and sparse representation,” IEEE Trans. Geosci. Remote Sens., vol. 54(4), pp. 1990-2000, Nov. 2015, doi: 10.1109/TGRS.2015.2493201
  • [11] W. Xie et al., "Spectral adversarial feature learning for anomaly detection in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens., vol. 58(4), pp. 2352-2365, Nov. 2019, doi: 10.1109/TGRS.2019.2948177.
  • [12] T. Zhou and D. Tao, "Godec: Randomized low-rank & sparse matrix decomposition in noisy case,” Proc. 28th Int. Conf. Machine Learn. (ICML), 2011, pp. 33-40.
  • [13] W. Sun et al., "Low-rank and sparse matrix decomposition-based anomaly detection for hyperspectral imagery,” J. Appl. Remote Sens., vol. 8, no. 1, pp. 083641, 2014, doi: 10.1117/1.JRS.8.083641
  • [14] G. Lerman and T. Maunu, "An overview of robust subspace recovery,” Proc. of IEEE, vol. 106(8), pp. 1380-1410, Aug. 2018, doi: 10.1109/JPROC.2018.2853141
  • [15] F. Küçük, B. Töreyin and F. V. Çelebi, "Sparse and low-rank matrix decomposition-based method for hyperspectral anomaly detection," J. Appl. Remote Sens., vol. 13, no. 1, pp. 014519, Feb. 2019, doi: 10.1117/1.JRS.13.014519.
  • [16] F. Küçük, B. U. Töreyin, F. V. Çelebi, "Anomaly detection in hyperspectral data with matrix decomposition," in: 26th Signal Processing and Communications Applications Conference, SIU, 2018, pp. 1–4, doi: 10.1109/SIU.2018.8404658.
  • [17] F. Küçük, "Hybrid anomaly detection method for hyperspectral images," Signal Image Video Process., vol. 17, pp. 2755-2761, Jan. 2023, doi: 10.1007/s11760-023-02492-4.
  • [18] F. Verdoja and M. Grangetto, "Graph Laplacian for image anomaly detection," Mach. Vis. Appl., vol. 31, no. 1–2, Jan. 2020, doi: 10.1007/s00138-020-01059-4.
  • [19] F. Zhang, F. He, and H. Hu, "Laplacian matrix graph for anomaly target detection in hyperspectral images," Elec. Lett., vol. 58(8), pp. 312-314, Feb. 2022, doi: 10.1049/ell2.12449.
  • [20] L. J. Grady and J. R. Polimeni, Discrete Calculus: Applied Analysis on Graphs for Computational Science. London, UK, Springer, 2010.
There are 20 citations in total.

Details

Primary Language English
Subjects Image Processing
Journal Section Research Articles
Authors

Fatma Küçük 0000-0002-7052-362X

Publication Date March 31, 2024
Submission Date July 7, 2023
Published in Issue Year 2024 Issue: 056

Cite

IEEE F. Küçük, “HYPERSPECTRAL ANOMALY DETECTION WITH AN IMPROVED APPROACH: INTEGRATION OF GO DECOMPOSITION ALGORITHM AND LAPLACIAN MATRIX MODIFIER”, JSR-A, no. 056, pp. 36–44, March 2024, doi: 10.59313/jsr-a.1324375.
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