Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
Boardman, J.W., Kruse, F.A., Green, R.O.: Mapping target signatures via partial unmixing of AVIRIS data (1995)
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)
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)
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)
Dobigeon, N., et al.: Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery. IEEE Trans. Sig. Proc. 57(11), 4355–4368 (2009)
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)
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)
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)
Somers, B., et al.: Endmember variability in spectral mixture analysis: a review. Remote Sens. Environ. 115(7), 1603–1616 (2011)
Robert, C., George, C.: Monte Carlo statistical methods. Springer Science and Business Media, New York (2013)
Andrieu, C., et al.: An introduction to MCMC for machine learning. Mach. Learn. 50(1–2), 5–43 (2003)
Feiyn, Z., et al.: Structured sparse method for hyperspectral unmixing. ISPRS J. Photogrammetry Remote Sens. 88, 101–118 (2014)
Moussaoui, S., et al.: On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation. Neurocomputing 71(10), 2194–2208 (2008)
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)
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)
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Figliuzzi, B., Velasco-Forero, S., Bilodeau, M., Angulo, J. (2016). A Bayesian Approach to Linear Unmixing in the Presence of Highly Mixed Spectra. In: Blanc-Talon, J., Distante, C., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2016. Lecture Notes in Computer Science(), vol 10016. Springer, Cham. https://doi.org/10.1007/978-3-319-48680-2_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-48680-2_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48679-6
Online ISBN: 978-3-319-48680-2
eBook Packages: Computer ScienceComputer Science (R0)