Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

TL;DR

This paper introduces a Bayesian method for simultaneous endmember extraction and abundance estimation in hyperspectral images, leveraging hierarchical modeling and Gibbs sampling for improved accuracy.

Contribution

It presents a unified Bayesian framework that jointly estimates endmembers and abundances, incorporating physical constraints and using Gibbs sampling for inference.

Findings

Accurate endmember and abundance estimation demonstrated on synthetic data.

Effective application to real AVIRIS hyperspectral images.

Outperforms traditional separate estimation methods.

Abstract

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images.