Recursive Hyperspectral Band Processing of Orthogonal Subspace Projection

Abstract

Progressive hyperspectral band processing (PHBP) processes data band by band without waiting for data to be completely collected according to the band-sequential (BSQ) format acquired by a hyperspectral imaging sensor. It provides progressive band-varying profiles for data processing. In order for PHBP to be implemented in real time, a recursive version of PHBP, called recursive hyperspectral band processing (RHBP), can also be derived by a concept similar to that of a Kalman filter. With such a Kalman filter-like RHBP, a real-time capability can be realized. This is particularly important for satellite communication when data download is limited by bandwidth and transmission. In Chap. 15 a commonly used subpixel target detection algorithm, the automatic target generation process (ATGP), presented in Sect. 4.4.2.3, is developed when the only required knowledge is the desired target signature. This chapter follows a similar treatment to extend another widely used mixed pixel classification technique, orthogonal subspace projection (OSP) developed by Harsanyi and Chang (IEEE Trans Geosci Remote Sens 32(4):779–785, 1994), to an RHBP version that can process OSPs band by band progressively to produce progressive band-varying profiles for various targets of interest. Unlike RHBP-anomaly detection (Chap. 14), which requires no target knowledge at all, RHBP-constrained energy minimization (Chap. 13), which requires only the desired target information as partial knowledge, and RHBP-ATGP (Chap. 15), which generates a set of targets of interest without prior knowledge, RHBP-OSP actually makes use of complete target knowledge provided a priori by known information or by unsupervised target finding algorithms such as ATGP a posteriori to produce a progressive band-varying profile of the abundance fraction of each target signature of interest for further band-by-band mixed pixel classification. Such progressive band-varying profiles offered by RHBP-OSP cannot be provided by any other OSP-like operator. Finally and most importantly, RHBP-OSP can locate and identify bands that are significant for data processing in a progressive manner, and the results can be updated only by innovation information generated by recursive equations. As a consequence, no accumulated computer processing time is required by RHBP to process all bands, and the time of processing each new incoming band is nearly constant.