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Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model

Altmann, Yoann and Dobigeon, Nicolas and Tourneret, Jean-Yves Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model. (2013) IEEE Transactions on Image Processing, 22 (4). 1267-1276. ISSN 1057-7149

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Official URL: http://dx.doi.org/ 10.1109/TIP.2012.2210235


This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér–Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.

Item Type:Article
Additional Information:Thanks to IEEE editor. The original publication is available at http://ieeexplore.ieee.org/
HAL Id:hal-00786063
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
Deposited On:07 Feb 2013 15:23

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