Augmented GBM Nonlinear Model to Address Spectral Variability for Hyperspectral Unmixing

Abstract

Spectral unmixing (SU) is a significant preprocessing task for handling hyperspectral images (HSI), but its process is affected by nonlinearity and spectral variability (SV). Currently, SV is considered within the framework of linear mixing models (LMM), which ignores the nonlinear effects in the scene. To address that issue, we consider the effects of SV on SU while investigating the nonlinear effects of hyperspectral images. Furthermore, an augmented generalized bilinear model is proposed to address spectral variability (abbreviated AGBM-SV). First, AGBM-SV adopts a generalized bilinear model (GBM) as the basic framework to address the nonlinear effects caused by second-order scattering. Secondly, scaling factors and spectral variability dictionaries are introduced to model the variability issues caused by the illumination conditions, material intrinsic variability, and other environmental factors. Then, a data-driven learning strategy is employed to set sparse and orthogonal bases for the abundance and spectral variability dictionaries according to the distribution characteristics of real materials. Finally, the alternating direction method of multipliers (ADMM) optimization method is used to split and solve the objective function, enabling the AGBM-SV algorithm to estimate the abundance and learn the spectral variability dictionary more effectively. The experimental results demonstrate the comparative superiority of the AGBM-SV method in both qualitative and quantitative perspectives, which can effectively solve the problem of spectral variability in nonlinear mixing scenes and to improve unmixing accuracy.