Keywords: Hyper spectral Data , feature Extraction, Principal Component Transform, Fourier Transform, Wavelet Decomposition.

Abstract:
Recently due to the advance of image scanning technology , hyper spectral image scanners which have tens or even hundreds spectral bands have been invented. Comparing to the traditional multispectral images, hyper spectral images include richer and finer spectral information than the images we can obtain, before. Theoretically, using hyper spectral images should increase our abilities in classifying land use/cover types. However, when traditional classification technologies are applied to process hyper spectral images, people are usually disappointed at the consequences of low efficiency, needing a large amount of training data, and hard improvement of classification accuracy. In order to solve this problem, our attention in the paper is focused on dimensionality reduction by feature selection or extraction. In this paper, we propose two new methods for feature extraction and compare with other feature extraction methods which have been developed from some other proposed papers. Finally, a practical AVIRIS data are analyzed to illustrate our discovery and test to show the efficiency of the new feature extraction methods.

1. Introduction
Multispectral sensors have been widely used to observe Earth surface since the 1960's. however, traditional sensors can only collect spectral data less than 20 bands due to the inadequate sensor technology. In recent years, spectral image sensors have been improved to collect spectral data in several hundreds bands, which are called hyper spectral image scanners. For example, the AVRIS scanners developed by JPL of NASA provide 224 contiguous spectral channels. Theoretically, using hyper spectral images should increase our abilities in classifying land use/cover types. However, the data classification approach that has been successfully applied to multispectral data in the past is not as effective for hyper spectral data as well.

As the dimensionality of the feature space increase subject to the number of bands, the number of training samples needed for image classification has to increase too. If training samples are insufficient for the need, which is quite common for the case of using hyper spectral data, parameters estimation becomes inaccurate. The classification accuracy first grows and then declines as the number of spectral bands increases, which is often referred to as the Hughes phenomenon (Hughes, 1968), see Figure 1.

Figure 1 Mean Recognition Accuracy vs. Measurement Complexity for the finite training case (Hughes phenomenon)
Generally speaking, classification performance depends on four factors: class separability, the training sample size, dimensionality, and classifier type (Hsien, 1998). To improve classification performance, our attention in the paper is focused on dimensionality reduction. Dimensionality reduction can be achieved in two different ways (Young and Fu, 1986). The first approach is to select a small subset of features which could contribute to class separability or classification criteria. This dimensionality reduction process is referred to as feature selection or band selection. The other approach is to use all the data from original feature space and map the effective features and useful information to a lower-dimensional subspace. This method is referred to as feature extraction. The goal of employing feature extraction is to remove the redundant information substantially without sacrificing significant information.

In this paper, we introduce a new concept of feature extraction which would transfer the spectral data from the original-feature space to a frequency-feature space. The frequency characteristics provide some useful information about the oscillation of the spectral curve for each pixel. Different type of materials can be distinguished on the basis of the differences in frequency variation. The methods we used in this study are called Fourier. Feature Extraction (FFE) and Wavelet Feature Extraction (WFE). FEE uses the global frequency characteristics of the spectral data and WFE are expected to be more meaningful and more stable than that formed by principle component transformation (PCT), which is commonly used in feature extraction.

This paper first review some feature extraction method which have been developed to speed up the process and increase the precision of classification. After, that the FEE and WFE methods are described. Finally, a 220-band AVIRIS data are analyzed to illustrate our discovery and test to show the efficiency of the new feature extraction methods.

2. Feature Selection
In feature selection, features that do not contribute to the discrimination of classes can be removed by assessing some criteria. Feature selection can not be preformed indiscriminately. Methods must be devised that allow the relative worth of features to be assessed in a quantitative and rigorous way. A procedure commonly used is to determine the separability of different classes (Richards, 1986). Separability is a measure of probabilistic distance or within classes. The separability commonly used in feature selection is Mahalanobis, Divergence, Transformed Divergence, Bhattacharya, or Jeffries-Matusita, etc (Schowengerdt, 1997).

A separability analysis can be performed on the training data to estimate the expected error in the classification for various feature combinations (Swain and Davis, 1978). Suppose the number of spectral bands is n, the problem of feature selection is to select the optimal subset of m with m<n. The number of feature combinations that need to be considered equals n!/(n-m)!m!. this number is too large for hyper spectral data and leads low efficiency in computation. Some algorithms such as Branch-and-Bound algorithm, Sequential Backward and max-Min Feature selection which can determine the optimal or suboptimal feature set were proposed to be computational feasible (Young and Fu, 1986).