A Bayesian Approach to Linear Unmixing in the Presence of Highly Mixed Spectra

  • Bruno FigliuzziEmail author
  • Santiago Velasco-Forero
  • Michel Bilodeau
  • Jesus Angulo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10016)


In this article, we present a Bayesian algorithm for endmember extraction and abundance estimation in situations where prior information is available for the abundances. The algorithm is considered within the framework of the linear mixing model. The novelty of this work lies in the introduction of bound parameters which allow us to introduce prior information on the abundances. The estimation of these bound parameters is performed using a simulated annealing algorithm. The algorithm is illustrated by simulations conducted on synthetic AVIRIS spectra and on the SAMSON dataset.


Bayesian Approach Prior Information Simulated Annealing Algorithm Bayesian Algorithm Gibbs Sampling Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported by the European Commission project M3S (Molecular Signature Detection with Multi-modal Microscopy Scanner) under the ICT PSP Call (Contract no. 621152). The authors would like to thank MEDyC team from Reims University for providing Raman spectra used in the experimental part. Special thanks also go to Jacques Klossa (TRIBVN) for discussion.


  1. [Bi]
    Bioucas-Dias, J.M., 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
  2. [Bo]
    Boardman, J.W., Kruse, F.A., Green, R.O.: Mapping target signatures via partial unmixing of AVIRIS data (1995)Google Scholar
  3. [Wi]
    Winter, M.E.: N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data. In: SPIE’s International Symposium on Optical Science, Engineering, and Instrumentation. International Society for Optics and Photonics (1999)Google Scholar
  4. [Na]
    Nascimento, J.M.P., Bioucas Dias, J.M.: Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens. 43(4), 898–910 (2005)CrossRefGoogle Scholar
  5. [Cha]
    Chang, C.-I., et al.: A new growing method for simplex-based endmember extraction algorithm. IEEE Trans. Geosci. Remote Sens. 44(10), 2804–2819 (2006)CrossRefGoogle Scholar
  6. [Dob]
    Dobigeon, N., et al.: Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery. IEEE Trans. Sig. Proc. 57(11), 4355–4368 (2009)MathSciNetCrossRefGoogle Scholar
  7. [Tho]
    Thouvenin, P.-A., Dobigeon, N., Tourneret, J.-Y.: Hyperspectral unmixing with spectral variability using a perturbed linear mixing model. IEEE Trans. Sig. Proc. 64(2), 525–538 (2016)MathSciNetCrossRefGoogle Scholar
  8. [Hal]
    Halimi, A., Dobigeon, N., Tourneret, J.-Y.: Unsupervised unmixing of hyperspectral images accounting for endmember variability. IEEE Trans. Image Proc. 24(12), 4904–4917 (2015)MathSciNetCrossRefGoogle Scholar
  9. [Zar]
    Zare, A., Ho, K.C.: Endmember variability in hyperspectral analysis: addressing spectral variability during spectral unmixing. IEEE Sig. Proc. Mag. 31(1), 95–104 (2014)CrossRefGoogle Scholar
  10. [Som]
    Somers, B., et al.: Endmember variability in spectral mixture analysis: a review. Remote Sens. Environ. 115(7), 1603–1616 (2011)CrossRefGoogle Scholar
  11. [Rob]
    Robert, C., George, C.: Monte Carlo statistical methods. Springer Science and Business Media, New York (2013)zbMATHGoogle Scholar
  12. [And]
    Andrieu, C., et al.: An introduction to MCMC for machine learning. Mach. Learn. 50(1–2), 5–43 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. [Fyz]
    Feiyn, Z., et al.: Structured sparse method for hyperspectral unmixing. ISPRS J. Photogrammetry Remote Sens. 88, 101–118 (2014)CrossRefGoogle Scholar
  14. [Mou]
    Moussaoui, S., et al.: On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation. Neurocomputing 71(10), 2194–2208 (2008)CrossRefGoogle Scholar
  15. [Moh]
    Mohan, A., Sapiro, G., Bosch, E.: Spatially coherent nonlinear dimensionality reduction and segmentation of hyperspectral images. IEEE Geosci. Remote Sens. Lett. 4(2), 206–210 (2007)CrossRefGoogle Scholar
  16. [Cas]
    Castrodad, A., et al.: Learning discriminative sparse representations for modeling, source separation, and mapping of hyperspectral imagery. IEEE Trans. Geosci. Remote Sens. 49(11), 4263–4281 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Bruno Figliuzzi
    • 1
    Email author
  • Santiago Velasco-Forero
    • 1
  • Michel Bilodeau
    • 1
  • Jesus Angulo
    • 1
  1. 1.Center for Mathematical Morphology, Mines ParisTechPSL Research UniversityFontainebleauFrance

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