Recursive Band Processing of Fast Iterative Pixel Purity Index

Abstract

As noted in Chap. 19, the performance of the pixel purity index (PPI) is largely determined by the number of skewers, K, to be used to calculate PPI counts for data sample vectors. Recently, two approaches were investigated. One is the iterative PPI (IPPI), developed by Chang and Wu [IEEE J Sel Top Appl Earth Obs Remote Sens 8(6):2676–2695, 2015], where Chap. 19 develops a progressive version of the IPPI, called progressive hyperspectral band processing of IPPI (PHBP-IPPI), and a recursive version of IPPI, called recursive hyperspectral band processing of IPPI (RHBP-IPPI), both of which vary with bands rather than skewer sets according to the band-sequential (BSQ) acquisition format so that bands can be collected band by band while data processing is taking place. Another approach is the fast iterative PPI (FIPPI) developed by Chang and Plaza [IEEE Geosci Remote Sens Lett 3(1):63–67, 2006] to address two major issues arising in PPI: the use of skewers whose number must be determined a priori and inconsistent final outcomes resulting from the use of skewers, which cannot be reproduced. FIPPI is an iterative algorithm that iterates each process until it reaches a final set of endmembers. Most importantly, it is an unsupervised algorithm, as opposed to the PPI, which requires human intervention to manually select a final set of endmembers. As shown in Chang and Plaza [IEEE Geosci Remote Sens Lett 3(1):63–67, 2006] and Chang and Wu [IEEE J Sel Top Appl Earth Obs Remote Sens 8(6):2676–2695, 2015] both the FIPPI and an IPPI produce very similar results, but FIPPI converges very rapidly with significant savings in computation. Following a similar treatment derived for RHBP-IPPI in Chap. 19, this chapter extends FIPPI to an RHBP version for FIPPI, called recursive hyperspectral band processing of FIPPI (RHBP-FIPPI) in such a way that data analysts can observe the progressive profiles of interband changes among bands produced by RHBP-FIPPI. The idea of implementing RHBP-FIPPI is to use two loops specified by skewers and bands implemented in RHBP-IPPI in Chap. 19 to process FIPPI. Depending on which one is implemented in the outer loop, two different versions of RHBP-FIPPI can be designed. When the outer loop is iterated band by band, it is called RHBP-FIPPI. When the outer loop is iterated by growing skewers, it is called recursive skewer processing of FIPPI (RSP-FIPPI). Interestingly, both versions provide different insights into the design of FIPPI but produce close results. Finally, note that since RHBP is implemented bandwise band by band, it does not require dimensionality reduction like the original FIPPI.