A fast alternative for the pixel purity index algorithm

We present a fast alternative for the popular pixel purity index (PPI) algorithm. This multi-dimensional PPI (MDPPI) algorithm is based on iteratively identifying convex hull indices in low-dimensional random projections. The MDPPI algorithm can yield identical results as the PPI algorithm, but several orders of magnitude faster. Furthermore, we show that the PPI algorithm is simply the MDPPI algorithm used in one dimension. In this work, we focus mainly on an efficient computational implementation of the algorithm. An ENVI implementation which can be used as a drop-in replacement of the standard PPI algorithm will be made available, along with a Matlab implementation.