Bayesian nonlinear hyperspectral unmixing with spatial residual component analysis

TL;DR

This paper introduces a Bayesian nonlinear unmixing method for hyperspectral images that models spatial correlations and nonlinearities, using an adaptive MCMC algorithm for improved estimation and inference.

Contribution

It proposes a novel hierarchical Bayesian model with spatially correlated nonlinear terms and an adaptive MCMC algorithm for hyperspectral unmixing.

Findings

Effective in modeling nonlinear and spatial effects

Outperforms state-of-the-art methods on synthetic data

Demonstrates robustness on real hyperspectral images

Abstract

This paper presents a new Bayesian model and algorithm for nonlinear unmixing of hyperspectral images. The model proposed 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.