Bayesian Nonlinear Hyperspectral Unmixing With Spatial Residual Component Analysis

Yoann Altmann, Marcelo Pereyra, Steve McLaughlin

Research output: Contribution to journalArticle (Academic Journal)peer-review

28 Citations (Scopus)
357 Downloads (Pure)


This paper presents a new Bayesian model and algorithm for nonlinear unmixing of hyperspectral images. The proposed model represents the pixel reflectances as linear combinations of the endmembers, corrupted by nonlinear (with respect to the endmembers) terms and additive Gaussian noise. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters and their constraints. In particular, a gamma Markov random field is used to model the joint distribution of the nonlinear terms, which are expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed to compute the Bayesian estimates of interest and perform Bayesian inference. This algorithm is equipped with a stochastic optimisation adaptation mechanism that automatically adjusts the parameters of the gamma Markov random field by maximum marginal likelihood estimation. Finally, the proposed methodology is demonstrated through a series of experiments with comparisons using synthetic and real data and with competing state-of-the-art approaches.
Original languageEnglish
Pages (from-to)174 - 185
Number of pages11
JournalIEEE Transactions on Computational Imaging
Issue number3
Publication statusPublished - 23 Sept 2015


  • Hyperspectral imagery
  • nonlinear spectral unmixing
  • residual component analysis
  • Gamma Markov random field
  • Bayesian estimation


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  • 8092 EPSRC D063485

    Nason, G. P.

    1/08/16 → …

    Project: Research

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