Recursive Hyperspectral Band Processing of Iterative Pixel Purity Index

The pixel purity index (PPI) is a very popular endmember finding algorithm due to its availability in ENvironment for Visualizing Images software. It is discussed in Chang (Hyperspectral data processing: algorithm design and analysis. Hoboken, 2013) in great detail, where various versions of PPI are developed from an algorithmic implementation point of view. Most recently, PPI was further expanded into the iterative PPI (IPPI) by Chang and Wu (IEEE J Sel Top Appl Earth Obs Remote Sens 8(6):2676–2695, 2015) with details also discussed in Chang (Real time progressive hyperspectral image processing: endmember finding and anomaly detection. New York, 2016). All such developments of PPI and IPPI are derived according to a data acquisition format, band-interleaved-by-pixel/sample (BIP/BIS), where data sample vectors are collected with full band information by a hyperspectral imaging sensor. This chapter takes a different approach to designing IPPI from another data acquisition point of view, called the band-sequential (BSQ) format, which allows users to process IPPI bandwise without waiting for full bands of data information to be collected. BIP/BIS and BSQ are the two types of data acquisition formats generally used to acquire hyperspectral imagery (Remote sensing: models and methods for image processing, New York, 1997). Basically, IPPI is suitable for both data acquisition formats. Interestingly, designing an IPPI using the BSQ format has not received attention to date. To make it work, IPPI must be capable of calculating and updating PPI counts of data sample vectors band by band. Intuitively, it seems that could be easily done. Unfortunately, several major challenging issues arise. Unlike many other hyperspectral imaging algorithms that only deal with sample vectors and bands by visualizing their progressive changes in algorithmic performance in a three-dimensional (3D) plot, IPPI has an extra parameter, called skewers, which are randomly generated vectors, that needs to be specified. By including skewers as a third parameter in addition to sample vectors and bands, PPI counts will require a four-dimensional plot to visualize progressive changes in PPI counts in a 3D parameter space specified by sample vectors, bands, and skewers. In this chapter we introduce a new concept for implementing IPPI band by band in a progressive manner called progressive hyperspectral band processing of IPPI (PHBP-IPPI) to address these issues by developing bandwise calculation of PPI counts of sample vectors sample by sample and bandwise calculation of PPI counts of sample vectors skewer by skewer. To further facilitate the use of PHBP-IPPI in practical applications, recursive equations are also derived for PHBP-IPPI to be used in the development of recursive hyperspectral band processing of IPPI (RHBP-IPPI), which can process data not only progressively but also recursively in a more efficient and effective manner, particularly in hardware design. As a result, many benefits can be gained from RHBP-IPPI. For example, it provides progressive profiles of IPPI counts of data samples recursively as more bands are included for data processing, finds crucial bands according to progressive changes in PPI counts, and detects significant bands for specific applications.