Hyperspectral Data Processing: Algorithm Design and Analysis

22.2 Dynamic Dimensionality Allocaction

The DDA presented in this section is designed to dynamically determine the values of q and . It originates from the pigeon-hole principle described in Section 1.3.2 as well as variable-length coding from the information theory. According to the pigeon-hole principle each signature is assumed as a pigeon to be accommodated by a particular spectral dimension/band which can be considered as a pigeon-hole. Therefore, the number of pigeons should determine at least how many pigeon-holes required for accommodation. This is equivalent to saying that the number of spectrally distinct signatures determines the minimal number of spectral dimensions/bands required for signature discrimination, which is exactly the original idea of VD. To materialize DDA, we first interpret the use of a pigeon-hole to accommodate a pigeon by a binary bit “1” and “0” otherwise. This implies that a spectral dimension/band being used to specify a particular signature will be encoded by “1.” Otherwise, “0” will be assigned to an unused spectral dimension/band. To fit the profile of source coding, the first task is to determine what type of signatures that can be considered as source alphabets. If the signature knowledge is provided a priori, this known signatures can be used as desired source alphabets. If there is no prior knowledge available about the data, the signatures ...