Sparsity Constrained Graph Regularized NMF for Spectral Unmixing of Hyperspectral Data

  • Roozbeh RajabiEmail author
  • Hassan Ghassemian
Research Article


Hyperspectral images contain mixed pixels due to low spatial resolution of hyperspectral sensors. Mixed pixels are pixels containing more than one distinct material called endmembers. The presence percentages of endmembers in mixed pixels are called abundance fractions. Spectral unmixing problem refers to decomposing these pixels into a set of endmembers and abundance fractions. Due to non negativity constraint on abundance fractions, non negative matrix factorization methods (NMF) have been widely used for solving spectral unmixing problem. In this paper we have used graph regularized NMF (GNMF) method combined with sparseness constraint to decompose mixed pixels in hyperspectral imagery. This method preserves the geometrical structure of data while representing it in low dimensional space. Adaptive regularization parameter based on temperature schedule in simulated annealing method also has been used in this paper for the sparseness term. Proposed algorithm is applied on synthetic and real datasets. Synthetic data is generated based on endmembers from USGS spectral library. AVIRIS Cuprite dataset is used as real dataset for evaluation of proposed method. Results are quantified based on spectral angle distance (SAD) and abundance angle distance (AAD) measures. Results in comparison with other methods show that the proposed method can unmix data more effectively. Specifically for the Cuprite dataset, performance of the proposed method is approximately 10 % better than the VCA and Sparse NMF in terms of root mean square of SAD.


Hyperspectral imaging Spectral unmixing Nonnegative matrix factorization (NMF) Graph regularization Sparseness constraint 



The authors would like to thank the associate editor for handling this paper and the anonymous reviewers for their valuable and helpful comments and suggestions.


  1. Alizadeh, H., & Ghassemian, H. (2012). Hyperspectral data unmixing using constrained semi-NMF and PCA transform. In 20th Iranian Conference on Electrical Engineering (ICEE), 15–17 May 2012 (pp. 1523–1527). doi: 10.1109/IranianCEE.2012.6292600.
  2. Bendoumi, M. A., & Mingyi, H. (2013). Unmixing approach for hyperspectral data resolution enhancement using high resolution multispectral image with unknown spectral response function. In Industrial Electronics and Applications (ICIEA), 2013 8th IEEE Conference on, 19–21 June 2013 (pp. 511–515). doi: 10.1109/ICIEA.2013.6566422.
  3. Cai, D., He, X., Han, J., & Huang, T. S. (2011). Graph regularized nonnegative matrix factorization for data representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(8), 1548–1560.CrossRefGoogle Scholar
  4. Chen, J., Richard, C., & Honeine, P. (2013). Nonlinear unmixing of hyperspectral data based on a linear-mixture/nonlinear-fluctuation model. IEEE Transactions on Signal Processing, 61(2), 480–492. doi: 10.1109/TSP.2012.2222390.CrossRefGoogle Scholar
  5. Cichocki, A., & Zdunek, R. (2006). Multilayer nonnegative matrix factorisation. Electronics Letters, 42(16), 947–948.CrossRefGoogle Scholar
  6. Cichocki, A., Zdunek, R., & Amari, S. I. (May 2006). New Algorithms for Non-Negative Matrix Factorization in Applications to Blind Source Separation. In IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006, 14–19 (Vol. 5, pp. V-V). doi: 10.1109/ICASSP.2006.1661352.
  7. Clark, R. N., Swayze, G. A., Wise, R., Livo, E., Hoefen, T., Kokaly, R., Sutley, S. J. (2007). USGS digital spectral library splib06a [Digital Data Series 231].
  8. Heinz, D. C., & Chang, C.-I. (2001). Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery. IEEE Transactions on Geoscience and Remote Sensing, 39(3), 529–545.CrossRefGoogle Scholar
  9. Keshava, N. (2003). A survey of spectral unmixing algorithms. Lincoln Lab Journal, 14(1), 55–78.Google Scholar
  10. Li, C., & Yin, J. (2013). A multispectral remote sensing data spectral unmixing algorithm based on variational Bayesian ICA. Journal of the Indian Society of Remote Sensing, 41(2), 259–268. doi: 10.1007/s12524-012-0245-0.CrossRefGoogle Scholar
  11. Ma, W.-K., Bioucas-Dias, J. M., Chan, T.-H., Gillis, N., Gader, P., Plaza, A., Ambikapathi, A., & Chi, C.-Y. (2014). Signal processing perspective on hyperspectral unmixing. IEEE Signal Processing Magazine, 31(1), 67–81.Google Scholar
  12. Miao, L., & Qi, H. (2007). End member extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization. IEEE Transactions on Geoscience and Remote Sensing, 45(3), 765–777. doi: 10.1109/tgrs.2006.888466.CrossRefGoogle Scholar
  13. Nascimento, J. M. P., & Dias, J. M. B. (2005). Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Transactions on Geoscience and Remote Sensing, 43(4), 898–910.CrossRefGoogle Scholar
  14. Pauca, V. P., Piper, J., & Plemmons, R. J. (2006). Nonnegative matrix factorization for spectral data analysis. Linear Algebra and Its Applications, 416(1), 29–47. doi: 10.1016/j.laa.2005.06.025.CrossRefGoogle Scholar
  15. Qian, Y., Jia, S., Zhou, J., & Robles-Kelly, A. (2011). Hyperspectral unmixing via L1/2 sparsity-constrained nonnegative matrix factorization. IEEE Transactions on Geoscience and Remote Sensing, 49(11), 4282–4297.CrossRefGoogle Scholar
  16. Rajabi, R., & Ghassemian, H. (2013). Hyperspectral data unmixing using GNMF method and sparseness constraint. In IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2013),, Melbourne, Australia, IEEE.Google Scholar
  17. Rajabi, R., & Ghassemian, H. (2011). Graph regularized nonnegative matrix factorization for hyperspectral data unmixing. Tehran: 7th Iranian Machine Vision and Image Processing (MVIP 2011).CrossRefGoogle Scholar
  18. Remon, A., Sanchez, S., Bernabe, S., Quintana-Orti, E., & Plaza, A. (2013). Performance versus energy consumption of hyperspectral unmixing algorithms on multi-core platforms. EURASIP Journal on Advances in Signal Processing, 2013(1), 68.CrossRefGoogle Scholar
  19. Sanjeevi, S., & Barnsley, M. J. (2000). Spectral unmixing of compact airborne spectrographic imager (CASI) data for quantifying sub-pixel proportions of biophysical parameters in a coastal dune system. Journal of the Indian Society of Remote Sensing, 28(2–3), 187–204. doi: 10.1007/bf02989903.CrossRefGoogle Scholar
  20. Villa, A., Chanussot, J., Benediktsson, J. A., & Jutten, C. (2011). Spectral unmixing for the classification of hyperspectral images at a finer spatial resolution. IEEE Journal of Selected Topics in Signal Processing, 5(3), 521–533.CrossRefGoogle Scholar
  21. Yang, Z., Zhou, G., Xie, S., Ding, S., Yang, J.-M., & Zhang, J. (2011). Blind spectral unmixing based on sparse nonnegative matrix factorization. IEEE TRANSACTIONS ON IMAGE PROCESSING, 20(4), 1112–1125. doi: 10.1109/tip.2010.2081678.CrossRefGoogle Scholar

Copyright information

© Indian Society of Remote Sensing 2014

Authors and Affiliations

  1. 1.ECE DepartmentTarbiat Modares UniversityTehranIran

Personalised recommendations