Estimating the Number of Endmembers in Hyperspectral Images Using the Normal Compositional Model and a Hierarchical Bayesian Algorithm

• Published in: IEEE journal of selected topics in signal processing Vol. 4; no. 3; pp. 582 - 591
• Main Authors: Eches, Olivier, Dobigeon, Nicolas, Tourneret, Jean-Yves
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2010; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Bayesian analysis; Bayesian inference; Bayesian methods; Composite materials; Computer Science; Computer simulation; Conducting materials; Data Structures and Algorithms; Estimates; hyperspectral images; Hyperspectral imaging; Hyperspectral sensors; Inference algorithms; Mathematical models; Monte Carlo methods; normal compositional model; Pixel; Pixels; Principal component analysis; reversible jump; Signal processing algorithms; spectral unmixing; Uncertainty; Reversible jump - Spectral unmixing; Monte Carlo methods; Hyperspectral images; Bayesian inference; Normal compositional model
• ISSN: 1932-4553; 1941-0484; 1941-0484
• DOI: 10.1109/JSTSP.2009.2038212

This paper studies a semi-supervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers . However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances ) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images.