By Donald A. Neamen

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One promising approach is the use of the following pigeon-hole principle described in the following section. 2 Pigeon-Hole Principle: Natural Interpretation of Hyperspectral Imaging Suppose that there are p pigeons flying into L pigeon holes (nests) with L < p. According to the pigeon-hole principle, there exists at least one pigeon hole that must accommodate at least two or more pigeons. Now, assume that L is the total number of spectral bands and p is the number of targets of interest. By virtue of the pigeon-hole principle, we can interpret a pigeon hole as a spectral band while a pigeon is considered as a target (or an object) of interest.

With this interpretation Chapter 32 extends results in Chapter 31 to MR image analysis. 6 Laboratory Data to be Used in This Book Three sets of laboratory data will be used for experiments in this book, two of which were collected by the airborne visible infrared imaging spectrometer (AVIRIS) and the third one is a gas data set. 1 Laboratory Data One data set to be used in this book is the one used in Harsanyi and Chang (1994). 5 mm and 158 bands after the water bands are removed. 9. 5 mm. gov/ chemistry.

In order to materialize this idea, three issues need to be addressed. First, the number of spectral bands, L, must be greater than or equal to the number of targets of interest, p, that is, L ! p. This seems always true for hyperspectral imagery, but is not 6 Hyperspectral Data Processing: Algorithm Design and Analysis necessarily valid for multispectral imagery, where L < p in the latter is usually true. For example, 3-band SPOT multispectral data may have difficulty with classifying more than three target substances present in the data using the pigeon-hole principle.

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