Nonlinear Spectral Unmixing of Hyperspectral Images Using Gaussian Processes

• Published in: IEEE transactions on signal processing Vol. 61; no. 10; pp. 2442 - 2453
• Main Authors: Altmann, Yoann, Dobigeon, Nicolas, McLaughlin, Steve, Tourneret, Jean-Yves
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2013; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Bayesian methods; Computer Science; Data Structures and Algorithms; Detection, estimation, filtering, equalization, prediction; Estimation; Exact sciences and technology; Gaussian processes; Hyperspectral imaging; Information, signal and communications theory; Manifolds; Materials; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; spectral unmixing; Telecommunications and information theory; Vectors; Performance evaluation; State of the art; spectral unmixing; Hyperspectral imagery; Non linear function; Unsupervised classification; Algorithm; Signal classification; Spectral signature; Hyperspectral imaging sensor; Gaussian process; Gaussian processes; Signal processing; Robustness; Bayes methods; hyperspectral imaging; Reflectance; Spectral unmixing; Hyperspectral imaging
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2013.2245127

This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method estimates the abundance vectors for all the image pixels using a Bayesian approach an a Gaussian process latent variable model for the nonlinear function (relating the abundance vectors to the observations). The endmembers are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is first evaluated on synthetic data. The proposed method provides accurate abundance and endmember estimations when compared to other linear and nonlinear unmixing strategies. An interesting property is its robustness to the absence of pure pixels in the image. The analysis of a real hyperspectral image shows results that are in good agreement with state of the art unmixing strategies and with a recent classification method.