A Complexity Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing

Abstract

Hyperspectral unmixing, as a blind source separation (BSS) problem, has been intensively studied from independence aspect in the last few years. However, independent component analysis (ICA) can not totally unmix all the materials out because the sources (abundance fractions) are not statistically independent. In this paper a complexity constrained nonnegative matrix factorization (CCNMF) for simultaneously recovering both constituent spectra and correspondent abundances is proposed. Three important facts are exploited: First, the spectral data are nonnegative; second, the variation of the material spectra and abundance images is smooth in time and space respectively; third, in most cases, both of the material spectra and abundances are localized. Experimentations on real data are provided to illustrate the algorithm's performance.