Stochastic Ml Estimation For Hyperspectral Unmixing Under Endmember Variability And Nonlinear Models

Hyperspectral unmixing (HU) is a problem of blindly identifying the underlying materials, in form of spectral signatures, in the captured hyperspectral image. HU has received tremendous interest in remote sensing, and fundamentally the problem can be regarded as solving a simplex-structured matrix factorization problem. The majority of HU research has been focused on the linear mixture model. On the other hand, remote sensing research has long indicated that real-life hyperspectral images can exhibit spatial variant and nonlinear effects. In this study we introduce a probabilistic approach for HU under two different models, namely, the normal composition model for modeling spatial endmember variability and the generalized bilinear model for modeling multi-path nonlinear effects. Our approach formulates HU as a maximum-likelihood (ML) model parameter estimation problem, and we demonstrate that the ML formulation can flexibly handle the two models. The ML problem is technical challenging, and we apply a combination of techniques, namely, sample average approximation, block coordinate descent and majorization-minimization, to tackle the problem. Our empirical study suggests that the ML method gives competitive recovery performance.