MULTI-DIMENSIONAL PIXEL PURITY INDEX

A popular algorithm for endmember extraction in hyperspectral imagery is the pixel purity index (PPI) algorithm, although it suffers from a large computational cost. In this paper, we show that the PPI algorithm can be interpreted as a Monte-Carlo integration of a partitioning of the unit sphere, induced by the convex hull of the data set. This interpretation allows us to develop a multi-dimensional extension of the PPI algorithm, which employs a much more efficient sampling process for this numerical integration, and hence converges much faster to the limiting solution. The resulting multi-dimensional pixel purity index algorithm is shown to be up to two orders of magnitude faster than the original PPI algorithm, while extracting the same endmembers.