Null Subspace Analysis for Spectral Unmixing in Hyperspectral Remote Sensing

Hyperspectral remote sensing is a new and fast growing remote sensing technology that is currently being investigated by researchers and scientists. A great challenge in hyperspectral image analysis is decomposing a mixed pixel into a collection of endmembers and their corresponding abundance fractions, namely spectral unmixing. This paper introduces null subspace to the process of spectral unmixing. Null subspace is the orthogonal complement space of the subspace spanned by some endmembers. Take advantage of null subspace, this paper presents a solution of obtaining the distance from a pixel to subspace in the null subspace form. By analysis on the null subspace, all endmembers in the hyperspectral image can be extracted by the maximal distance criterion and the abundance can be obtained by the way of distance proportion. In the experiment, it shows that null subspace provides a fast and effective way for spectral unmixing.