Hyperspectral unmixing using double-constrained multilayer NMF

Hyperspectral unmixing (HU) refers to the process decomposing the entire hyperspectral image into a set of endmembers and the corresponding abundance fractions. Nonnegative matrix factorization (NMF) has been widely used in HU due to its simplicity and effectiveness. Many extensions of NMF have been also developed since traditional NMF has a large solution space. On the other hand, the multilayer structure has shown great advantages in learning data representation. Inspired by these considerations, we added sparsity and geometric structure constraints to the multilayer NMF structure and proposed a double-constrained multilayer NMF (DCMLNMF) method for HU in this paper. The multilayer NMF structure was obtained by iteratively decomposing the target matrix into a number of layers. To improve the unmixing performance, a sparsity constraint term on the abundance matrix and a graph regularization term were both incorporated to each layer. Besides, a layer-wise optimization method based on Nesterov's optimal gradient method was further proposed to solve the multi-factor NMF problem. Experimental results based on both synthetic data and real data demonstrate that the proposed method outperforms several other state-of-art approaches.