High-order statistics-based approaches to endmember extraction for hyperspectral imagery

Endmember extraction has received considerable interest in recent years. Many algorithms have been developed for this purpose and most of them are designed based on convexity geometry such as vertex or endpoint projection and maximization of simplex volume. This paper develops statistics-based approaches to endmember extraction in the sense that different orders of statistics are used as criteria to extract endmembers. The idea behind the proposed statistics-based endmember extraction algorithms (EEAs) is to assume that a set of endmmembers constitute the most un-correlated sample pool among all the same number of signatures with correlation measured by statistics which include variance specified by 2^nd order statistics, least squares error (LSE) also specified by 2^nd order statistics, skewness 3^rd order statistics, kurtosis 4^th order statistics, k^th moment and statistical independency specified by infinite order of statistics measured by mutual information. In order to substantiate proposed statistics-based EEAs, experiments using synthetic and real images are conducted for demonstration.