Design and Development of Iterative Pixel Purity Index

Pixel purity index (PPI) and N-finder algorithm (N-FINDR) are the two most widely used techniques for finding endmembers in hyperspectral imagery. Unfortunately, both of them suffer from two same major issues, inconsistency resulting from random initial conditions and computational complexity resulting from finding all endmembers simultaneously. To resolve these issues, a theory of iterative N-FINDR (IN-FINDR) has been recently developed for N-FINDR via iterative processes. This paper develops various versions of iterative PPI (IPPI), which can be considered as a companion paper of IN-FINDR. The IPPI reinvents a wheel by redesigning various versions of iterative algorithms which implement PPI via two iterative processes, one for data sample vectors and the other for skewers. More specifically, two different iterative versions of IPPI are developed, called progressive IPPI (P-IPPI) and causal IPPI (C-IPPI), which correspond to two versions of IN-FINDR, successive N-FINDR (SC N-FINDR) and sequential N-FINDR (SQ N-FINDR), respectively. Because they are iterative in nature, C-IPPI and P-IPPI can be further extended to process skewer sets in two different fashions, varying skewer set and growing skewer set, to be called varying skewer set C-IPPI (VC-IPPI) and growing skewer set P-IPPI (GP-IPPI). As a result, the fast IPPI (FIPPI) can be shown indeed to be their special case.