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Nonlinear Dimensionality Expansion to Multispectral Imagery

Hyperspectral imaging sensors have been around more than two decades. Interestingly, there is no cut-and-dried definition available in the literature to differentiate hyperspectral imagery from multispectral imagery. A general understanding of distinction between these two is that a hyperspectral image is acquired by hundreds of “contiguous” spectral channels/bands with very fine spectral resolution, while a multispectral image is collected by tens of “discrete” spectral channels/bands with low spectral resolution. If this interpretation is used, we then run into a dilemma, “how many spectral channels are sufficiently enough for a remotely sensed image to be called a hyperspectral image?” or “how fine the spectral resolution should be for a remote sensing image to be considered as a hyperspectral image?” For example, if we take a small set of hyperspectral band images with spectral resolution 10 nm, say five band images, to form a five-dimensional image cube, do we still consider this newly formed five-dimensional image cube as a hyperspectral image or simply a multispectral image? If we adopt the former definition based on the number of bands, this five-dimensional image cube should be viewed as a multispectral image. On the other hand, if we adopt the latter definition based on spectral resolution, the five-dimensional image cube should be considered as a hyperspectral image. So, which one is correct? Thus far, it seems that there is no general consensus to settle this issue. This chapter makes an attempt to address this issue from a perspective of linear spectral mixture analysis (LSMA) via the pigeon-hole principle described in Chapter 1 so that a multispectral imaging (MSI) can be explored in such a way that hyperspectral imaging (HSI) can also be applicable to multispectral imagery. Two approaches are introduced in this chapter for such an exploration, both of which can be considered as reverse operations of data dimensionality reduction discussed in Chapter 6. One is band expansion process (BEP) originated from the band generation process (BGP) proposed by Ren and Chang (2000a), which can be viewed as a reverse process of dimensionality reduction by band selection (DRBS) in Chapter 6. The resulting LSMA is called band dimesnionality expansion (BDE)-based LSMA. The other is feature dimensionality expansion (FDE) derived from the kernel-based approaches discussed in Chapters 2 and 13. The resulting LSMA is then called kernel-based LSMA.