Hyperspectral Data Processing: Algorithm Design and Analysis

1.8 Notations and Terminologies to be Used in this Book

Since this book primarily deals with real hyperspectral data, the image pixels are generally mixed and not necessarily pure. The term “endmember” is not used here; instead, a general term “signature” or “signature vector” is used. In addition, because we are only interested in target analysis, the term “targets” instead of “materials” is also used throughout this book. In order to make a distinction between a target pixel and its spectral signature vector, we use notation “t” to represent the target pixel vector, “r” for an image pixel vector, and “s” or “m” to indicate its spectral signature vector. We also use bold uppercase for matrices and bold lowercase for vectors. The italic upper case “L” will be used for the total number of spectral bands, K for the sample spectral covariance matrix, and R for the sample spectral correlation matrix. Also, δ^∗(r) is used to represent a detector or classifier that operates on an image pixel vector r where the superscript “∗” in δ^∗(r) specifies what type of a detector or classifier to be used. It should be noted that δ^∗(r) is a real-valued function that takes a form of inner product of a filter vector w with r, that is, with the filter vector w^∗ specified by a particular detector or classifier. We also use “α”and to represent the abundance vector and its estimate where the notation “hat” ...