| New sensor technology provides higher spectral and spatial resolution enabling a greater number of spectrally separate classes to be identified. The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) system, for example, collects image data in 220 spectral bands covering 0.4--2.5 mum wavelength regions with 20 m spatial and 10 mum spectral resolution. As a result, hyperspectral data analysis, is a laborious and time consuming problem to deal with. Unfortunately, the acquisition of the labeled samples needed for designing the classifier remain a difficult and expensive job. Ill-conditioned and even ill-posed problems arise due to small p dimensional training sample size.; It is the main goal of this investigation the application of regularization techniques for the selection of an optimum regularization parameter per class when limited training samples causes covariance estimators to become highly variable. An optimum regularization parameter for each known class will be developed by simultaneously minimizing the probability of error and the probability of false alarm. The effect of regularization on the probability of outliers in a high dimensional space will be considered as well. |
