Hyperspectral Imagery

The generalized bilinear model (GBM) generalizes both the linear mixing model and recently introduced bilinear models by including second-order interaction terms between endmembers. A hierarchical Bayesian algorithm with Metropolis-within-Gibbs sampling ensures positivity and sum-to-one constraints.

Abundance maps from GBM unmixing

This unsupervised Bayesian algorithm models pixels as linear combinations of random endmembers weighted by abundances, generalizing the normal compositional model. It estimates both mean and covariance matrix for each endmember, quantifying material behavior and variability across the scene.

Spectral variability of endmembers across the scene

Three hyperspectral mixture models with Bayesian algorithms for supervised unmixing. Based on residual component analysis, the general formulation assumes the linear model corrupted by additive terms accounting for nonlinearities, endmember variability, or mismodeling effects.

Residual component analysis for robust unmixing

Endmember variability and mismodelling effects

Two novel hyperspectral mixture models and unmixing algorithms. The nonlinearity model generalizes bilinear models by including higher order interaction terms. The alternating direction method of multipliers (ADMM) solves the convex problem with theoretical convergence guarantees.

Fast unmixing via ADMM with convergence guarantees

Correntropy-based cost functions provide robustness to outliers in hyperspectral unmixing, down-weighting large residual errors compared to standard least-squares cost.

The proposed noise-whitened eigen-gap approach achieves near-perfect accuracy across all noise overestimation levels, significantly outperforming existing methods.

Noise-whitened eigen-gap approach for intrinsic dimension estimation