Region-Based Estimate of Endmember Variances for Hyperspectral Image Unmixing

Endmember variability is receiving growing attention in the hyperspectral image (HSI) unmixing field. As an extension of linear mixing model (LMM), normal compositional model (NCM) assumes that the pixels of the HSI are linear combinations of random endmembers (as opposed to deterministic for the LMM). NCM explains spectral differences between the observed pixels and endmembers as endmember mixtures and endmember variances, the characteristic of which makes it possible to incorporate the endmember spectral variability in the unmixing process. But the tricky issue for using NCM is the estimation of endmember variances inhering in materials. This letter presents a new approach, termed region-based stochastic expectation maximization, to learn endmember variances from spatial information. The idea is assuming that significant homogeneous regions (composed of similar materials or similar mixture) exist in the HSI, such regions usually give visual indication that spatial-based spectral variability really exists in hyperspectral data. As modeled in NCM, spectral variances in homogeneous region can be approximately linear represented by endmember variances. Hence, given region-based spectral variances, we are able to learn endmember variances. In experiments with simulated data and Moffett field data, the proposed approach competes with other unmixing methods considering endmember variability, with better endmember variance estimates.