Band subset selection for hyperspectral imaging

This chapter extends band selection (BS) in Chapter 4, which selects bands one at a time to band subset selection (BSS), which selects multiple bands simultaneously as a band subset. The key issue arising in BSS but not in BS is that BSS requires exhausting all possible band subsets to find an optimal band subset, which is practically infeasible. The BSS to be presented in this chapter reinvents a wheel by interpreting each selected band as a desirable endmember from an endmember-finding viewpoint so that finding an optimal band subset is equivalent to finding an optimal set of endmembers. Its idea is to first use virtual dimensionality (VD) to determine the number of multiple bands to be selected as a band subset, n _BS. Then, BSS is performed by two iterative processes, sequential band subset selection (SQBSS) and successive band subset selection (SCBSS), both of which are designed based on two recently endmember-finding algorithms derived from N-finder (N-FINDR), sequential N-FINDR (SQ N-FINDR), and successive N-FINDR (SC N-FINDR). As a result, the traditional single band-based BS can be considered as a special case of BSS with a band subset considered to be a singleton set where SQBSS and SCBSS are reduced to band search algorithms according to a specific criterion determined by a particular application. In this chapter, we are particularly interested in extending the constrained band selection (CBS) presented in Chapter 4 to constrained band subset selection BSS (CBSS) which can be considered as the counterpart of CBS. Interestingly, we can also derive two versions of CBSS, called multiple band-constrained BSS (MBC-BSS) and multiple target-constrained BSS (MTC-BSS) in correspondence to the two versions of CBS, band constrained BS (BCBS) and target-constrained BS (TCBS). Nevertheless, two key differences between BCBS/TCBS and MBC-BSS/MTC-BSS are (i) prior knowledge n_BS and (ii) BSS search algorithms, both of which are required for BSS but not necessarily needed for BS.