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FEATURE EXTRACTION OF HYPERSPECTRAL IMAGES 
USING MATCHING PURSUIT 
P.H. Hsu 
Associate Research Fellow, National Science and Technology Center for Disaster Reduction, 
106, No. 200, Sec. 3, Hsinhai Rd., Taipei, Taiwan, Republic of China - paihui(g)naphm.ntu.edu.tw 
TS Ths 5 
KEY WORDS: Hyper-Spectral Sensing, Wavelet Transform, Matching Pursuit, Feature Extraction, Classification 
ABSTRACT: 
Hyperspectral images contain rich and fine spectral information, an improvement of land use/cover classification accuracy is 
expected from the use of such images. However, the classification methods that have been successfully applied to multispectral data 
in the past are not as effective as to hyperspectral data. The major cause is that the size of training data set does not correspond to the 
increase of dimensionality of hyperspectral data. Actually, the problem of the “curse of dimensionality” emerges when a statistic- 
based classification method is applied to the hyperspectral data. A simpler, but sometimes very effective way of dealing with 
hyperspectral data is to reduce the number of dimensionality. This can be done by feature extraction that a small number of salient 
features are extracted from the hyperspectral data when confronted with a limited set of training samples. In this paper, we tested 
some proposed feature extraction methods based on the wavelet transform to reduce the high dimensionality without losing much 
discriminating power in the new feature space. In addition, a new feature extraction method based on the matching pursuit with 
wavelet packet is used to extract useful features for classification. An AVIRIS data set was tested to illustrate the classification 
performance of the new method and be compared with the existing wavelet-based methods of feature extraction. 
I. INTRODUCTION 
Since the mid 1980s, the new technology of imaging 
spectrometer with two-dimensional area arrays of detector 
elements was developed to collect spectral data with a large 
number of bands simultaneously (Goetz ef al., 1985). The value 
of this technique lies in the ability to construct an effectively 
continuous reflectance spectrum for each pixel of the sense. 
Because of the large number of spectral bands, the images 
acquired with imaging spectrometers are also referred to as 
hyperspectral images which are distinguished from the 
multispectral images with only three to ten bands. The rich and 
detailed spectral information provided by hyperspectral images 
can be used to identify and quantify a large range of surface 
materials which cannot be identified by multispectral images. 
By means of the solar reflected spectrum measured by imaging 
spectrometers, a wide range of scientific researches and 
applications have being proposed based on the spectral analysis 
(Lillesand and Kiffer, 2000). 
1.1 Curse of Dimensionality 
Seemingly the high dimensionality of hyperspectral data should 
increase the abilities and effectiveness in classifying land 
use/cover types. However, the classification methods that have 
been successfully applied to multispectral data in the past are 
not as effective as to hyperspectral data. The major cause is that 
the size of training data set does not adapt to the increasing 
dimensionality of hyperspectral data. If the training samples are 
insufficient for the needs, which is common for the 
hyperspectral case, the estimation of statistical parameters 
becomes inaccurate and unreliable. As the dimensionality 
increases with the number of bands, the number of training 
samples needed for training a specific classifier should be 
increased exponentially as well. The rapid increase in training 
883 
samples size for density estimation has been termed the “curse 
of dimensionality” by Bellman (1961), which leads to the 
“peaking phenomenon” or “Hughes phenomenon” in classifier 
design (Hughes, 1968). The consequence is that the 
classification accuracy first grows and then declines as the 
number of spectral bands increases while training samples are 
kept the same. For a given classifier, the "curse of 
dimensionality” can only be avoided by providing a sufficiently 
large sample size. The more complex the classifier, the larger 
should the ratio of sample size to dimensionality be to avoid the 
curse of dimensionality. However, in practice, the number of 
training samples is limited in most of the hyperspectral 
applications. Furthermore, the high dimensionality of 
hyperspectral data makes it necessary to seek new analytic 
methods to avoid a vast increase in the computational time. A 
simpler, but sometimes very effective way of dealing with high- 
dimensional data is to reduce the number of dimensions (Lee 
and Landgrebe, 1993; Benediktsson er a/., 1995; Landgrebe, 
2001). This can be done by feature selection or extraction that a 
small number of salient features are extracted from the 
hyperspectral data when confronted with a limited set of 
training samples. 
1.2 Spectral Feature Extraction 
Feature extraction is generally considered a data mapping 
procedure which determines an appropriate subspace of 
dimensionality M from the original feature space of 
dimensionality N ( M<N ) (Fukunaga, 1990; Lee and 
Landgrebe, 1993; Jain et al, 2000). The way of feature 
extraction can be a linear or nonlinear data transformation. 
Regardless of how the data transformation is implemented, the 
feature extraction algorithm must be designed to preserve the 
information of interest for a special problem such as 
compression, denoising, or classification. For example, in