A PROJECTED GRADIENT-BASED ALGORITHM TO UNMIX HYPERSPECTRAL DATA

This paper presents a method to solve hyperspectral unmixing problem based on the well-known linear mixing model. Hyperspectral unmixing is to decompose observed spectrum of a mixed pixel into its constituent spectra and a set of corresponding abundances. We use Nonnegative Matrix Factorization (NMF) to solve the problem in a single step. The proposed method is based on a projected gradient NMF algorithm. Moreover, we modify the NMF algorithm by adding a penalty term to include also the statistical independence of abundances. At the end, the performance of the method is compared to two other algorithms using both real and synthetic data. In these experiments, the algorithm shows interesting performance in spectral unmixing and surpasses the other methods. Index Terms — Spectral unmixing, linear mixture model (LMM), non-negative matrix factorization (NMF), hyperspectral imagery. 1