Combinatorial Nonnegative Matrix-Tensor Factorization for Hyperspectral Unmixing Using a General $\ell _{q}$ Norm Regularization

Abstract

Hyperspectral unmixing (HU), an essential procedure for various environmental applications, has garnered significant attention within remote sensing communities. Among different groups of HU methods, non-negative matrix factorization (NMF)-based ones have gained widespread popularity due to their high capability in simultaneously extracting endmembers and their corresponding abundances. However, converting 3D hyperspectral data cube into 2D matrix format leads to the loss of spatial and potential correlation information. Consequently, in recent years, non-negative tensor factorization (NTF) methods, which preserve the 3D nature of hyperspectral data cube, have been extensively embraced by numerous researchers. Nevertheless, incorporating prior information into NTF-based problems faces limitations owing to the inconsistency of such information, particularly concerning ℓ1 norm sparsity and the abundance sum-to-one constraint (ASC). To address this limitation, our study introduces a novel general regularization term. This term leverages sparsity and ASC simultaneously, integrating it into a matrix-tensor factorization framework. Our proposed method, named matrix-tensor based hyperspectral unmixing method with general ℓq norm regularization (MTUHLq), is established on the block term decomposition (BTD) paradigm, which ensures physical interpretability and simple implementation. To investigate the performance of the proposed MTUHLq, a series of experiments on both synthetic and real hyperspectral data sets were conducted. The results of the implemented experiments indicated that the proposed method outperformed other stateof-the-art hyperspectral unmixing methods.