23

Progressive Band Selection

Both progressive spectral dimensionality process (PSDP) in Chapter 20 and progressive band dimensionality process (PBDP) in Chapter 21 are developed to prioritize spectral dimensions/bands and process spectral dimensions/bands in the context of progressive spectral dimension/band dimensionality expansion and reduction via dimensionality prioritization (DP)/band prioritization (BP). However, there is a key difference between PSDP and PBDP. In PSDP, “data compaction” is performed via a transformation of the original data space into a spectral-transformed component space where spectral components are of major interest and each spectral component is specified by a projection vector as a spectral component dimension. Such projection vectors are obtained by linearly combining all spectral band dimensions across the entire range of wavelengths. In contrast to PSDP, PBDP performs “data reduction” by retaining only those bands that are of interest and discarding the rest. As a result, there is no data processing involved in PBDP as it is in PSDP that processes the entire data cube by a transformation. This is why PSDP requires projection vectors to specify spectral components while PBDP does not, since the bands in PBDP can be considered a counterpart of projection vectors in PSDP. However, it is worth noting that projection vectors are completely different from spectral bands because the bands are acquired with individual and separate wavelengths with interband correlation yet to be explored, whereas projection vectors are obtained by a transformation using interband correlation. This crucial distinction leads to a new concept of progressive band selection (PBS), which implements PBDP in conjunction with band de-correlation (BD) whose counterpart is not found in PSDP (refer to Chapter 20). The need of BD arises from the fact that some highly prioritized bands may also share much information in common if their acquired wavelengths are very close in range. Such interband correlation among bands needs to be addressed by BD in PBDP, but this is not an issue for DR used in PSDP. So, despite that a concept similar to PBS can also be derived for progressive dimensionality reduction (PDR), Safavi (2010) has shown that not much gain could be benefited from PDR since much spectral dimensionality correlation has already been removed by mutual original projection vectors implemented by PSDP. Accordingly, this chapter focuses only on PBS; readers may refer to Safavi (2010) for the treatment of PDR.