Hyperspectral unmixing using sparsity-constrained multilayer non-negative matrix factorization

Abstract

Hyperspectral unmixing (HU) refers to the process of decomposing the hyperspectral image into a set of endmember spectra and the corresponding set of abundance fractions. Non-negative matrix factorization (NMF) has been widely used in HU. However, most NMF-based unmixing methods have single-decomposition structures, which may have poor performance for highly mixed and ill-conditioned data. We proposed a sparsity-constrained multilayer NMF (MLNMF) method for spectral unmixing of highly mixed data. The MLNMF structure was established by decomposing the abundance matrix layer-by-layer to acquire the endmember matrix and the abundance matrix in the next layer. To reduce the space of solutions, sparsity constraints were added to the multilayer model by incorporating an L1 regularizer to the abundance matrix in each layer. Moreover, a layerwise strategy based on the Nesterov’s optimal gradient method was also proposed to optimize the multifactor NMF problem. Experiments on both synthetic data and real data demonstrate that our proposed method outperforms several other state-of-art approaches.