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

TL;DR

This paper introduces an unsupervised nonlinear unmixing method for hyperspectral images using a polynomial post-nonlinear model and a Hamiltonian Monte Carlo algorithm for efficient parameter estimation, demonstrating high accuracy on synthetic and real data.

Contribution

It proposes a novel Bayesian nonlinear unmixing approach with a Hamiltonian Monte Carlo algorithm tailored for hyperspectral data, handling complex parameter constraints.

Findings

Effective unmixing on synthetic data

Accurate analysis of real hyperspectral images

Convergence and parameter tuning validated

Abstract

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 polynomials leading to a polynomial post-nonlinear 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.