Hyperspectral unmixing using nonnegative matrix factorization with an approximate L₀ sparsity constraint

Hyperspectral unmixing is a process to identify the constituent materials and estimate the corresponding abundance fractions from the mixture. A branch of existing unmixing algorithms is based on nonnegative matrix factorization (NMF), which has the advantage of low complexity and the ability to easily include physical constraints. As an important constraint for NMF, sparsity could be modeled using the L₀ norm. However, the application of the L ₀ regularizer is an NP hard optimization problem. This paper uses an approximate L₀ norm to model the sparseness of the abundances. Then, we use an alternate projected gradient algorithm to solve the proposed model. The experiments including both the synthetic data and the real data show the validity of the proposed method.