Kernel sparse NMF for hyperspectral unmixing

Spectral unmixing is one of the most challenging and fundamental problems in hyperspectral imagery. In this paper, we address a hyperspectral imagery unmixing problem by introducing sparse nonnegative matrix factorization unmixing algorithms into kernel space. Many sparse nonnegative matrix factorization algorithms has been recently applied to solve the hyperspectral unmixing problem because it overcome the difficulty of absence of pure pixels and sufficiently utilize the sparse characteristic of the data. Most existing sparse nonnegative matrix factorization algorithms for unmixing are based on the linear mixing models. In fact, hyperspectral data are more likely to lie on nonlinear model space. Motivated by the fact that kernel trick can capture the nonlinear structure of data during the decomposition, we propose a new hyperspectral imagery unmixing algorithm by introducing sparse nonnegative matrix factorization unmixing algorithms into kernel space in this paper. Experimental results based on synthetic hyperspectral data show the superiority of the proposed algorithm with respect to other state-of-the-art approaches.