Bi-Endmember Semi-NMF Based on Low-Rank and Sparse Matrix Decomposition

This article presents a bi-endmember semi-nonnegative matrix factorization (Semi-NMF) algorithm based on low-rank and sparse matrix decomposition (LRSMD), referred to as BLSNMF, to resolve the issues of endmember variability and nonlinear mixing. Given the fact that the hyperspectral images contain a large amount of redundant information, compressing sensing (CS) techniques can generally be used to randomly sense the effective information in an observed image according to the effective approximation of the bi-endmember components. In this article, the proposed BLSNMF integrates low-rank and sparse spaces decomposed by go decomposition (GoDec) or orthogonal subspace projection-based go decomposition (OSP-GoDec) with Semi-NMF to suppress interference between different components so as to improve the unmixing performance via a simple linear mixed model. Specifically, the observed data space is first decomposed by GoDec or OSP-GoDec to approximate four different attribute components, CS-sampled double low-rank components, structured sparse component, and noise component. Second, from the CS-sampled double low-rank components, the inherent and new endmembers along with their abundances are evaluated via Semi-NMF, and then, the double low-rank components are redescribed using the estimated endmembers and abundances. Finally, the serious interference entries in the structured sparse component space are removed from the data to better learn other attribute components. The experimental results show that BLSNMF can eliminate the interference of new endmembers and sparse noise so as to better evaluate the endmembers and abundances and effectively improve the ability to interpret the spectral information.