Estimating the Number of Endmembers to Use in Spectral Unmixing of Hyperspectral Data with Collaborative Sparsity

  • Lucas Drumetz
  • Guillaume Tochon
  • Jocelyn Chanussot
  • Christian Jutten
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10169)


Spectral Unmixing (SU) in hyperspectral remote sensing aims at recovering the signatures of the pure materials in the scene (endmembers) and their abundances in each pixel of the image. The usual SU chain does not take spectral variability (SV) into account, and relies on the estimation of the Intrinsic Dimensionality (ID) of the data, related to the number of endmembers to use. However, the ID can be significantly overestimated in difficult scenarios, and sometimes does not correspond to the desired scale and application dependent number of endmembers. Spurious endmembers are then frequently included in the model. We propose an algorithm for SU incorporating SV, using collaborative sparsity to discard the least explicative endmembers in the whole image. We compute an algorithmic regularization path for this problem to select the optimal set of endmembers using a statistical criterion. Results on simulated and real data show the interest of the approach.


Hyperspectral images Remote sensing Collaborative sparsity Alternating Direction Method of Multipliers Regularization path Bayesian Information Criterion 


  1. 1.
    Ammanouil, R., Ferrari, A., Richard, C., Mary, D.: Blind and fully constrained unmixing of hyperspectral images. IEEE Trans. Image Process. 23(12), 5510–5518 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bioucas-Dias, J., Nascimento, J.: Hyperspectral subspace identification. IEEE Trans. Geosci. Remote Sens. 46(8), 2435–2445 (2008)CrossRefGoogle Scholar
  3. 3.
    Bioucas-Dias, J., Plaza, A., Dobigeon, N., Parente, M., Du, Q., Gader, P., Chanussot, J.: Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches. IEEE J. Sel. Top. Appl. Earth Observations Remote Sens. 5(2), 354–379 (2012)CrossRefGoogle Scholar
  4. 4.
    Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)CrossRefzbMATHGoogle Scholar
  5. 5.
    Cawse-Nicholson, K., Damelin, S., Robin, A., Sears, M.: Determining the intrinsic dimension of a hyperspectral image using random matrix theory. IEEE Trans. Image Process. 22(4), 1301–1310 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Drumetz, L., Chanussot, J., Jutten, C.: Endmember variability in spectral unmixing: recent advances. In: Proceedings of IEEE Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), pp. 1–4 (2016)Google Scholar
  7. 7.
    Drumetz, L., Veganzones, M.A., Gómez, R.M., Tochon, G., Dalla Mura, M., Licciardi, G.A., Jutten, C., Chanussot, J.: Hyperspectral local intrinsic dimensionality. IEEE Trans. Geosci. Remote Sens. 54(7), 4063–4078 (2016)CrossRefGoogle Scholar
  8. 8.
    Drumetz, L., Veganzones, M.A., Henrot, S., Phlypo, R., Chanussot, J.: Jutten, C: Blind hyperspectral unmixing using an extended linear mixing model to address spectral variability. IEEE Trans. Image Process. 25(8), 3890–3905 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32(2), 407–499 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Heinz, D., Chang, C.I.: Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery. IEEE Trans. Geosci. Remote Sens. 39(3), 529–545 (2001)CrossRefGoogle Scholar
  11. 11.
    Heylen, R., Parente, M., Gader, P.: A review of nonlinear hyperspectral unmixing methods. IEEE J. Sel. Top. Appl. Earth Observations Remote Sens. 7(6), 1844–1868 (2014)CrossRefGoogle Scholar
  12. 12.
    Hu, Y., Chi, E., Allen, G.I.: ADMM algorithmic regularization paths for sparse statistical machine learning (2015). arXiv preprint arXiv:150406637
  13. 13.
    Iordache, M.D., Bioucas-Dias, J.M., Plaza, A.: Collaborative sparse regression for hyperspectral unmixing. IEEE Trans. Geosci. Remote Sens. 52(1), 341–354 (2014)CrossRefGoogle Scholar
  14. 14.
    Nascimento, J., Bioucas Dias, J.: Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens. 43(4), 898–910 (2005)CrossRefGoogle Scholar
  15. 15.
    Priestley, M.B.: Spectral Analysis and Time Series. Academic Press, London (1981)zbMATHGoogle Scholar
  16. 16.
    Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Veganzones, M.A., Drumetz, L., Marrero, R., Tochon, G., Dalla Mura, M., Plaza, A., Bioucas-Dias, J., Chanussot, J.: A new extended linear mixing model to address spectral variability. In: Proceedings of the IEEE Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (2014)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Lucas Drumetz
    • 1
  • Guillaume Tochon
    • 2
  • Jocelyn Chanussot
    • 1
  • Christian Jutten
    • 1
  1. 1.Univ. Grenoble Alpes, CNRS, GIPSA-labGrenobleFrance
  2. 2.EPITA Research and Development Laboratory (LRDE)Le Kremlin-BicêtreFrance

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