Unsupervised Post-Nonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm

Yoann Altmann (1) , Nicolas Dobigeon (1) , Jean-Yves Tourneret (2, 3)

1 IRIT-SC - Signal et Communications
2 IRIT-MINDS - CoMputational imagINg anD viSion
3 Toulouse INP - Institut National Polytechnique (Toulouse)

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are post-nonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using second-order polynomials leading to a polynomial postnonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient Hamiltonian Monte Carlo algorithm is investigated. The classical leapfrog steps of this algorithm are modified to handle the parameter constraints. The performance of the unmixing strategy, including convergence and parameter tuning, is first evaluated on synthetic data. Simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images.

Mots clés: Hyperspectral imagery; Hamiltonian Monte Carlo; Unsupervised spectral unmixing; Post-nonlinear model

Domaines: Informatique et langage [cs.CL]

Yoann Altmann, Nicolas Dobigeon, Jean-Yves Tourneret. Unsupervised Post-Nonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm. IEEE Transactions on Image Processing, 2014, 23 (6), pp.2663-2675. ⟨10.1109/TIP.2014.2314022⟩. ⟨hal-00992112⟩