Joint Bayesian Endmember Extraction and Linear Unmixing for Hyperspectral Imagery

• Published in: IEEE transactions on signal processing Vol. 57; no. 11; pp. 4355 - 4368
• Main Authors: Dobigeon, N., Moussaoui, S., Coulon, M., Tourneret, J.-Y., Hero, A.O.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Bayesian analysis; Bayesian inference; Bayesian methods; Computer Science; Computer simulation; Detection, estimation, filtering, equalization, prediction; Dissolved gas analysis; endmember extraction; Engineering Sciences; Exact sciences and technology; Extraction; hyperspectral imagery; Hyperspectral imaging; Imagery; Indexes; Information, signal and communications theory; Layout; linear spectral unmixing; Mathematical models; MCMC methods; Miscellaneous; Parameter estimation; Pixel; Samplers; Signal and communications theory; Signal and Image Processing; Signal processing; Signal processing algorithms; Signal, noise; Spectral analysis; Telecommunications and information theory; Bayes estimation; Airborne instruments; Hyperspectral imagery; Prior distribution; Gibbs sampling; Linear model; Hyperspectral imaging sensor; Accuracy; MCMC algorithm; Linear combination; Simulation; linear spectral unmixing; Signal processing; Thermal imaging; Bayes methods; Hierarchical system; Bayesian inference; endmember extraction; MCMC methods; Posterior distribution; Monte Carlo methods; Bayesian estimation; Endmember extraction; Spectral unmixing; Hyperspectral imaging
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2025797

This paper studies a fully Bayesian algorithm for endmember 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.