Bilinear Hyperspectral Unmixing via Tensor Decomposition

The bilinear mixture model (BMM) is often used in hyperspectral unmixing (HU) for incorporating nonlinear effects, which is considered more general than the widely used linear mixture model (LMM). Existing BMM-based HU methods often lack identifiability guarantees of the endmembers and their abundances unless some stringent conditions are met. This work puts forth a new framework for BMM-based HU. Our method models the hyperspectral image as a latent factor-structured block-term tensor decomposition model with multilinear rank
$(L_{r},\ L_{r},\ 1)$
terms (“LL 1” model for short). This way, the HU task boils down to finding the block terms of the tensor model. The LL 1 model's essential uniqueness naturally provides identifiability guarantees of the endmembers/abundances under reasonably mild conditions. An alternating gradient projection (GP) algorithm is proposed to takle the formulated tensor decomposition-based BMM-HU problem. Simulations on semi-real and real datasets show the high-quality unmixing performance of the proposed GP algorithm compared to state-of-the-art methods.