Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

  • Authors:
  • Nicolas Dobigeon;Saïd Moussaoui;Martial Coulon;Jean-Yves Tourneret;Alfred O. Hero

  • Affiliations:
  • IRIT/INP-ENSEEIHT, University of Toulouse, Toulouse Cedex 7, France and Department of EECS, University of Michigan, Ann Arbor, MI;IRCCyN, CNRS UMR, ECN, Nantes Cedex 3, France;IRIT/INP-ENSEEIHT, University of Toulouse, Toulouse Cedex 7, France;IRIT/INP-ENSEEIHT, University of Toulouse, Toulouse Cedex 7, France;Department of EECS, University of Michigan, Ann Arbor, MI

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2009

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Abstract

This paper studies a fully Bayesian algorithm for end-member extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for nonnegativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images.