Nonlinear Unmixing of Hyperspectral Images Using a Generalized Bilinear Model

• Published in: IEEE transactions on geoscience and remote sensing Vol. 49; no. 11; pp. 4153 - 4162
• Main Authors: Halimi, A., Altmann, Y., Dobigeon, N., Tourneret, J.
• Format: Journal Article
• Language: English
• Published: IEEE 01.11.2011; Institute of Electrical and Electronics Engineers
• Subjects: Bayesian algorithm; Bayesian methods; bilinear model; Computer Science; Gibbs sampler; hyperspectral imagery; Hyperspectral imaging; Markov chain Monte Carlo (MCMC) methods; Markov processes; Networking and Internet Architecture; Signal and Image Processing; Signal to noise ratio; spectral unmixing; Gibbs sampler; Bayesian algorithm; Hyperspectral imagery; Bilinear model; Markov chain Monte Carlo (MCMC) methods; Spectral unmixing
• ISSN: 0196-2892; 1558-0644; 1558-0644
• DOI: 10.1109/TGRS.2010.2098414

Nonlinear models have recently shown interesting properties for spectral unmixing. This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization not only of the accepted linear mixing model but also of a bilinear model that has been recently introduced in the literature. Appropriate priors are chosen for its parameters to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. Unfortunately, this posterior is too complex to obtain analytical expressions of the standard Bayesian estimators. As a consequence, a Metropolis-within-Gibbs algorithm is proposed, which allows samples distributed according to this posterior to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.