Factor-Regularized Nonnegative Tensor Decomposition for Blind Hyperspectral Unmixing

The hyperspectral unmixing (HU) aims at estimating the spectral signatures of endmembers (or materials) and their corresponding abundance maps of the hyperspectral image (HSI). In this work, we treat the HSI as an 3D cube and propose a new tensor-based HU method. We decompose an HSI data as the sum of several multilinear rank-(Lr, Lr, 1) terms (or LL1 model). Based on the fact that the latent factors of LL1 model are physical meaningful (i.e., abundance maps and spectral signatures), we build a nonnegative tensor decomposition optimization model with the low-rank constraint and impose an implicit regularizer to exploit the nonlocal self-similarity prior of abundance maps-whose related subproblem can be easily solved under the plug-and-play framework. We develop an alternating direction method of multipliers algorithm to solve the proposed model. Numerical experiments demonstrate the effectiveness of our algorithm.