Nonlinear spectral unmixing using residual component analysis and a Gamma Markov random field

This paper presents a new Bayesian nonlinear unmixing model for hyperspectral images. The proposed model represents pixel reflectances as linear mixtures of endmembers, corrupted by an additional combination of nonlinear terms (with respect to the endmembers) and additive Gaussian noise. A central contribution of this work is to use a Gamma Markov random field to capture the spatial structure and correlations of the nonlinear terms, and by doing so to improve significantly estimation performance. In order to perform hyperspectral image unmixing, the Gamma Markov random field is embedded in a hierarchical Bayesian model representing the image observation process and prior knowledge, followed by inference with a Markov chain Monte Carlo algorithm that jointly estimates the model parameters of interest and marginalises latent variables. Simulations conducted with synthetic and real data show the accuracy of the proposed SU and nonlinearity estimation strategy for the analysis of hyperspectral images.