A Constrained Non-Negative Matrix Factorization Approach to Unmix Highly Mixed Hyperspectral Data

This paper presents a blind source separation method to unmix highly mixed hyperspectral data, i.e., each pixel is a mixture of responses from multiple materials and no pure pixels are present in the image due to large sampling distance. The algorithm introduces a minimum volume constraint to the standard non-negative matrix factorization (NMF) formulation, referred to as the minimum volume constrained NMF (MVC-NMF). MVC-NMF explores two important facts: first, the spectral data are non-negative; second, the constituent materials occupy the vertices of a simplex, and the simplex volume determined by the actual materials is the minimum among all possible simplexes that circumscribe the data scatter space. The experimental results based on both synthetic mixtures and a real image scene demonstrate that the proposed method outperforms several state-of-the-art approaches.