title: Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery.
abstract: This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images.
authors.affiliation: University of Toulouse, IRIT/INP-ENSEEIHT/TéSA, 31071 Toulouse cedex 7, France. olivier.eches@enseeiht.fr
authors.forename: Olivier
authors.initials: O
authors.lastname: Eches
authors.forename: Nicolas
authors.initials: N
authors.lastname: Dobigeon
authors.forename: Corinne
authors.initials: C
authors.lastname: Mailhes
authors.forename: Jean-Yves
authors.initials: JY
authors.lastname: Tourneret
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016014:Linear Models; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted