Using blocks of skewers for faster computation of pixel purity index

Abstract

The “pixel purity index” (PPI) algorithm proposed by Boardman, et al1 identifies potential endmember pixels in multispectral imagery. The algorithm generates a large number of “skewers” (unit vectors in random directions), and then computes the dot product of each skewer with each pixel. The PPI is incremented for those pixels associated with the extreme values of the dot products. A small number of pixels (a subset of those with the largest PPI values) are selected as “pure” and the rest of the pixels in the image are expressed as linear mixtures of these pure endmembers. This provides a convenient and physically-motivated decomposition of the image in terms of a relatively few components. We report on a variant of the PPI algorithm in which blocks of B skewers are considered at a time. Prom the computation of B dot products, one can produce a much larger set of “derived” dot products that are associated with skewers that are linear combinations of the original B skewers. Since the derived dot products involve only scalar operations, instead of full vector dot products, they can be very cheaply computed. We will also discuss a hardware implementation on a field programmable gate array (FPGA) processor both of the original PPI algorithm and of the block-skewer approach. We will furthermore discuss the use of fast PPI as a front-end to more sophisticated algorithms for selecting the actual endmembers.