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Paper Count: 30855
Sparse Unmixing of Hyperspectral Data by Exploiting Joint-Sparsity and Rank-Deficiency
Abstract: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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1131429Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 463
 G. Shaw and D. Manolakis, “Signal processing for hyperspectral image exploitation”, IEEE Signal Process. Mag., vol.19, no.1, pp.12–16, 2002.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.