Unmixing of Hyperspectral Data Using Spectral Libraries

Abstract

In hyperspectral images, pixels are found as a mixture of the spectral signatures of several materials, especially when there is an insufficient spatial resolution. In recent years, spectral libraries have provided spectral information of hundreds of materials that allow the development of techniques to solve the problem of hyperspectral unmixing in a semi-supervised fashion. These methods which are also known as sparse regression techniques assume that mixed pixels are a sparse linear combination of spectral signatures of materials in already available spectral libraries. In this paper, the spectral mixing problem has been solved via sparse separation methods. The United States Geological Survey (USGS) spectral library is used to generate simulated hyperspectral data. A comparative analysis is performed to determine which material signatures in the library are mixed in the pixels by using the convex-relaxation-based sparse regression methods. Root Mean Square Error (RMSE), Signal to Reconstruction Error (SRE) and processing time of the algorithms are used as comparing criterions. Moreover, Hinton diagrams are used to visualize which material signatures are found in the library and the proportions of these found material signatures.

Keywords

• : Hyperspectral Imaging,Hyperspectral Unmixing,Sparse Regression,Sparse Unmixing,Spectral Library

References

1. Akhtar, N., Shafait, F., Mian, A. (2015). Futuristic greedy approach to sparse unmixing of hyperspectral data. IEEE Transactions on Geoscience and Remote Sensing, 53(4), 2157-2174.
2. Berman, M., Kiiveri, H., Lagerstrom, R., Ernst, A., Dunne, R., Huntington, J. F. (2004). ICE: A statistical approach to identifying endmembers in hyperspectral images. IEEE Transactions on Geoscience and Remote Sensing, 42(10), 2085-2095.
3. Bioucas-Dias, J. M., Figueiredo, M. A. (2010, June). Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing. In 2010 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (pp. 1-4). IEEE.
4. Bioucas-Dias, J. M., Plaza, A., Dobigeon, N., Parente, M., Du, Q., Gader, P., Chanussot, J. (2012). Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 5(2), 354-379.
5. Boardman, J. W., Kruse, F. A., Green, R. O. (1995). Mapping target signatures via partial unmixing of AVIRIS data.
6. Chen, S. S., Donoho, D. L., Saunders, M. A. (2001). Atomic decomposition by basis pursuit. SIAM review, 43(1), 129-159.
7. Elad, M. (2010). Sparse and redundant representations: from theory to applications in signal and image processing. Springer Science & Business Media.
8. Grant, M., Boyd, S. (2014). CVX: Matlab software for disciplined convex programming, version 2.1,[Online]. http://cvxr.com/cvx.

9. Heylen, R., Parente, M., Gader, P. (2014). A review of nonlinear hyperspectral unmixing methods. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 7(6), 1844-186
10. Iordache, M. D., Bioucas-Dias, J. M., Plaza, A. (2011). Sparse unmixing of hyperspectral data. IEEE Transactions on Geoscience and Remote Sensing, 49(6), 2014-2039.
11. Iordache, M. D., Bioucas-Dias, J. M., & Plaza, A. (2012). Total variation spatial regularization for sparse hyperspectral unmixing. IEEE Transactions on Geoscience and Remote Sensing, 50(11), 4484-4502.
12. Iordache, Marian-Daniel, Bioucas-Dias, Jose M, Plaza, Antonio, 2014. Collaborative sparse regression for hyperspectral unmixing. IEEE Transactions on Geoscience and Remote Sensing, 52, 341--354.
13. Keshava, N., & Mustard, J. F. (2002). Spectral unmixing. IEEE Signal Processing Magazine, 19(1), 44-57.
14. Kucuk, S, (2015). Target detection from long-wave infrared hyperspectral images. (Master's thesis). Hacettepe University, Ankara, Türkiye.
15. Kokaly, Raymond F, Clark, Roger N, Swayze, Gregg A, Livo, K Eric, Hoefen, Todd M, Pearson, Neil C, Wise, Richard A, Benzel, William M, Lowers, Heather A, Driscoll, Rhonda L et al., (2017). Usgs spectral library version 7. Technical report, US Geological Survey.
16. Li, J., Bioucas-Dias, J. M. (2008, July). Minimum volume simplex analysis: A fast algorithm to unmix hyperspectral data. In IGARSS 2008-2008 IEEE International Geoscience and Remote Sensing Symposium (Vol. 3, pp. III-250). IEEE.Mallat, S. G., Zhang, Z. (1993). Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41(12), 3397-3415.
17. Nascimento, J. M., Dias, J. M. (2005). Vertex component analysis: A fast algorithm to unmix hyperspectral data. IEEE transactions on Geoscience and Remote Sensing, 43(4), 898-910.
18. Papyan, V., Romano, Y., Sulam, J., Elad, M. (2018). Theoretical foundations of deep learning via sparse representations: A multilayer sparse model and its connection to convolutional neural networks. IEEE Signal Processing Magazine, 35(4), 72-89.
19. Pati, Y. C., Rezaiifar, R., Krishnaprasad, P. S. (1993, November). Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. In Proceedings of 27th Asilomar conference on signals, systems and computers (pp. 40-44). IEEE.
20. Shi, Z., Tang, W., Duren, Z., & Jiang, Z. (2014). Subspace matching pursuit for sparse unmixing of hyperspectral data. IEEE Transactions on Geoscience and Remote Sensing, 52(6), 3256-3274.
21. Toker, K. G., Yüksel, S. E. (2018, May). A greedy algorithm for sparse unmixing. In 2018 26th Signal Processing and Communications Applications Conference (SIU) (pp. 1-4). IEEE.
22. Winter, M. E. (1999, October). N-FINDR: An algorithm for fast autonomous spectral end-member determination in hyperspectral data. In Imaging Spectrometry V (Vol. 3753, pp. 266-275). International Society for Optics and Photonics.
23. Yuksel, S. E., Kucuk, S., Gader, P. D. (2016). SPICEE: An Extension of SPICE for Sparse Endmember Estimation in Hyperspectral Imagery. IEEE Geoscience and Remote Sensing Letters, 13(12), 1910-1914.
24. Zare, A., Gader, P. (2007). Sparsity promoting iterated constrained endmember detection in hyperspectral imagery. IEEE Geoscience and Remote Sensing Letters, 4(3), 446-450.
25. Zhang, Z., Xu, Y., Yang, J., Li, X., Zhang, D. (2015). A survey of sparse representation: algorithms and applications. IEEE access, 3, 490-530.