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

Yoann Altmann*, Nicolas Dobigeon, Jean-Yves Tourneret

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1267-1276
Number of pages10
JournalIEEE Transactions on Image Processing
Issue number4
Publication statusPublished - Apr 2013


  • Constrained Cramér-Rao bound
  • nonlinearity detection
  • post-nonlinear mixing model (PPNMM)
  • spectral unmixing (SU)

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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