Hyperspectral Data Processing: Algorithm Design and Analysis

33.1 Design Principles for Nonliteral Hyperspectral Imaging Techniques

Two principles, pigeon-hole principle and principle of orthogonality, have been backbones for designing and developing nonliteral hyperspectral imaging techniques presented in this book and Chang (2003a). While the pigeon-hole principle is a fundamental rule in discrete mathematics (Epp, 1995), the orthogonality principle is the most important criterion in designing mean squared error (MSE) estimation algorithms (Poor, 1994). If these two principles are intellectually interpreted to design algorithms, many new ideas and approaches will then follow naturally as described in the following.

33.1.1 Pigeon-Hole Principle

The pigeon-hole principle says that if p pigeons flying into L pigeon-holes (nests) with , then there exists at least one pigeon-hole that must accommodate at least two or more pigeons. So, if we interpret pigeons and pigeon-holes as material substances to be recognized and spectral bands, respectively, then a spectral band which is essentially a pigeon-hole can be used to accommodate a target substance, which is considered as a pigeon. In the following section, we described how this principle is used to interpret design rationales used for hyperspectral data processing.

33.1.1.1 Multispectral Imagery versus Hyperspectral Imagery

First, the pigeon-hole principle can be used to resolve a long-standing ...