Spectral Inter-Band Discrimination Capacity of Hyperspectral Imagery

This paper introduces a new concept of band capacity (BC) of a hyperspectral image and further develops a theory for BC. Its idea is derived from information theory where a band channel can be constructed from a hyperspectral image with both its channel input space and channel output space specified by its full band set and the channel transition probabilities between the input and output spaces characterized by between-band discrimination. In particular, a transition probability from a spectral band in the band channel input space to a spectral band in the band channel output space is calculated by their spectral discriminatory power/probability. By virtue of such a formulated band channel, its maximal mutual information can be defined as BC of a hyperspectral image to represent spectral discriminatory power per band measured by bits. Interestingly, BC provides a key to bridging the concept of virtual dimensionality defined as the number of spectrally distinct signatures and effective band dimensionality to be used to discriminate these spectrally distinct signatures one from another. Accordingly, an immediate application of BC is to determine the number of bands to be selected, n(BS). Another application is band selection with the output space specified by a selected n(BS)-band subset. In this case, when BC is close to one, the selected band set tends to be optimal.