Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32718
Sparse Unmixing of Hyperspectral Data by Exploiting Joint-Sparsity and Rank-Deficiency

Authors: Fanqiang Kong, Chending Bian


In this work, we exploit two assumed properties of the abundances of the observed signatures (endmembers) in order to reconstruct the abundances from hyperspectral data. Joint-sparsity is the first property of the abundances, which assumes the adjacent pixels can be expressed as different linear combinations of same materials. The second property is rank-deficiency where the number of endmembers participating in hyperspectral data is very small compared with the dimensionality of spectral library, which means that the abundances matrix of the endmembers is a low-rank matrix. These assumptions lead to an optimization problem for the sparse unmixing model that requires minimizing a combined l2,p-norm and nuclear norm. We propose a variable splitting and augmented Lagrangian algorithm to solve the optimization problem. Experimental evaluation carried out on synthetic and real hyperspectral data shows that the proposed method outperforms the state-of-the-art algorithms with a better spectral unmixing accuracy.

Keywords: Hyperspectral unmixing, joint-sparse, low-rank representation, abundance estimation.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 720


[1] G. Shaw and D. Manolakis, “Signal processing for hyperspectral image exploitation”, IEEE Signal Process. Mag., vol.19, no.1, pp.12–16, 2002.
[2] J. M. Bioucas-Dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches”, IEEE J. Sel.Topics Appl. Earth Observ. Remote Sens., vol.5, no. 2, pp. 354-379, 2012.
[3] M. Arngren, M. N. Schmidt, and J. Larsen, “Bayesian nonnegative matrix factorization with volume prior for unmixing of hyperspectral images”, in Proc. IEEE Int. Workshop MLSP, France: Grenoble, 2009, pp. 1-6.
[4] H. Pu, B. Wang, L. Zhang, “Simplex geometry-based abundance estimation algorithm for hyperspectral unmixing”, Scientia Sinica Infor-mationis, vol.42, no.8, pp.1019-1033, 2012.
[5] Y. Qian, S. Jia, J. Zhou, et al. “Hyperspectral unmixing via sparsity-constrained nonnegative matrix factorization”. Geoscience and Remote Sensing, IEEE Transactions on, 2011, vol.49, no.11, pp.4282-4297.
[6] M.-D. Iordache, J. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 6, pp.2014–2039, Jun. 2011.
[7] Z. Shi, W. Tang, Z. Duren, and Z. Jiang. "Subspace matching pursuit for sparse unmixing of hyperspectral data," IEEE Trans. Geosci. Remote Sens., vol.52, no.6, pp.3256-3274, Jun. 2013.
[8] J. M. Bioucas-Dias and M. A. T. Figueiredo, “Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing,” in Proc. 2nd WHISPERS, Jun. 2010, pp. 1–4.
[9] M. D. Iordache, J. Bioucas-Dias, and A. Plaza, “Total variation spatial regularization for sparse hyperspectral unmixing”, IEEE Trans. Geosci. Remote Sens., vol.50, no.11, pp. 4484-4502, Nov. 2012.
[10] M. D. Iordache, J. Bioucas-Dias and A. Plaza, “Collaborative sparse regression for hyperspectral unmixing”, IEEE Trans. Geosci. Remote Sens., vol. 52, no. 1, pp.341-354, Jan. 2014.
[11] S. Cotter, B. Rao, K. Engan, K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors”, IEEE Transactions on Signal Processing, vol.53, no.7, pp. 2477-2488, 2005.
[12] F. Kong, W. Guo, Y. Li, et al. “Backtracking-Based Simultaneous Orthogonal Matching Pursuit for Sparse Unmixing of Hyperspectral Data”. Mathematical Problems in Engineering, 2015, 2015:1-17.