Sparsity-Constrained Coupled Nonnegative Matrix–Tensor Factorization for Hyperspectral Unmixing

Abstract

Hyperspectral unmixing refers to a source separation problem of decomposing a hyperspectral imagery (HSI) to estimate endmembers, and their corresponding abundances. Recently, matrix–vector nonnegative tensor factorization (MV-NTF) was proposed for unmixing to avoid structure information loss, which is caused by the HSI cube unfolding in nonnegative matrix factorization (NMF)-based methods. However, MV-NTF ignores local spatial information due to directly dealing with data as a whole, meanwhile, the forceful rank constraint in low-rank tensor decomposition loses some detailed structures. Unlike MV-NTF works at the original data, the pixel-based NMF is more adaptive to learn local spatial variations. Hence, from the perspective of multi-view, it is significant to utilize the complementary advantages of MV-NTF and NMF to fully preserve the intrinsic structure information, and exploit more detailed spatial information. In this article, we propose a sparsity-constrained coupled nonnegative matrix-tensor factorization (SCNMTF) model for unmixing, wherein MV-NTF and NMF are subtly coupled by sharing endmembers and abundances. Since the representations for abundances in MV-NTF and NMF are distinct, abundance sharing is achieved indirectly by introducing an auxiliary constraint. Furthermore, the $L_{1/2}$ regularizer is adopted to promote the sparsity of abundances. A series of experiments on synthetic and real hyperspectral data demonstrate the effectiveness of the proposed SCNMTF method.