Sparsity-constrained generalized bilinear model for hyperspectral unmixing

Generalized bilinear model (GBM) has been widely used for nonlinear hyperspectral image unmixing. However, it does not take the sparse information of abundance into account, which is a significant characteristic resulting from the correlation of hyperspectral data. This paper aims to extend the GBM by incorporating the sparsity constraint of abundance matrix with the semi-nonnegative matrix factorization, by dividing GBM into the linear part and the second-order part, which are optimized using an alternating optimization algorithm respectively. L1/2-norm is used to explore the sparse characteristic, and the L1/2-constrained semi-nonnegative matrix factorization (L1/2-semi-NMF) algorithm is presented, which leads to better results on both synthetic and real data.