Multiscale Analysis of Hyperspectral Data
Using Wavelets for Spectral Feature Extraction
Pai-Hui Hsu Yi-Hsing Tseng
Department of Surveying Engineering,
National Cheng-Kung University
No.1 University Road, Tainan, Taiwan
Tel:+886-6-2370876 Fax: +886-6-2375764
E-mail: p6885101@sparc1.cc.ncku.edu.tw
TAIWAN
Keywords: Hyperspectral Data, Spectral Feature Extraction, Wavelet Transform
Abstract
The purpose of feature extraction is to abstract substantial information from the original data input and filter out redundant information. In this study, we transfer hyperspectral data from the original-feature space into a scale-space plane using the wavelet transform to extract the significant spectral features. The wavelet transform can focus on localized signal structures with a zooming procedure. The absorption bands are thus detected with the wavelet transform modulus maxima, and Lipschitz exponents are estimated at each singularity point of the spectral curve from the decay of the wavelet transform amplitude. The local frequency variances provide some useful information about the oscillations in the hyperspectral curve for each pixel. Various types of materials can be distinguished by the differences in the local frequency variation. This new method generates more features that are meaningful and is more stable than other known methods for spectral feature extraction.
1. Introduction
Multispectral imagery has been used for earth observation since the 1960's. Many effective methods of spectral data analysis have been developed for various applications. Although multispectral imagery has proved to be useful for earth observation, it frequently failed to differentiate similar land cover reflectance due to its low spectral resolution. Imaging spectrometry was developed to acquire images with high spectral resolution, which are commonly called hyperspectral images. These images typically have several hundred spectral bands, and so enable the construction of detail reflectance spectrum for each pixel (Lillesand and Kiffer, 2000). A typical example is the image obtained by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) developed by NASA JPL which has 224 contiguous spectral channels covering a spectral region form 0.4 to 2.5
mm with 10 nm bandwidth. Theoretically, using hyperspectral images should increase our abilities to identify various material types. However, the data classification approach that has been successfully applied to multispectral images in the past is not as effective with hyperspectral images. Most of the traditional methods for classification are statistically based on decision rules, which are determined by the known training samples. As the number of dimensions in the feature space increases, subject to the number of bands, the number of training samples needed for image classification also increases. If the number of training samples is insufficient, which is quite common in hyperspectral data cases, the statistical parameter 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).
In order to improve the classification performance, some of the approaches are based on statistical theory to extract important features from the original hyperspectral data prior to the classification processing. The goal of employing feature extraction is to substantially remove the redundant information without sacrificing significant information. Some proposed feature extraction methods are compared by the classification performance (Hsu and Tseng, 1999), such as principal component analysis (Schowengerdt, 1997), discriminant analysis feature extraction (Tadjudin and Landgrebe, 1998), and decision boundary feature extraction (Lee and Landgrebe, 1993). These methods are referred to as statistic-based feature extraction.
Due to the high spectral resolution of hyperspectral images, it becomes possible to analyze the diagnostic absorption and reflection characteristics of an object over narrow wavelength intervals. For example, the spectral reflectance curves of healthy green vegetation manifests a "peak-and-valley" configuration (Lillesand and Kiffer, 2000). The absorption and reflection characteristics are often related to the internal structure of the materials. Some approaches were proposed to locate and characterize these subtle spectral details. Piech et. al. (1987) used the symbolic descriptions of spectral features, called fingerprints, as quantitative indices of the absorption bands to distinguish various materials. Derivative analysis (Demetriades-Shah et. al., 1990; Philpot, 1991; Tsai and Philpot, 1997) of hyperspectral data makes use of the fact that the derivative of a function tends to emphasize changes irrespective of the mean level (Tsai and Philpot, 1998). Techniques that can detect more meaningful spectral features that are related to physical attributes are called physical-related feature extraction methods.
In this study, we attempted to transform the spectral data from the original feature space into a scale-space plane using the wavelet transform. The wavelet transform (WT) can focus on localized signal structures with a zooming procedure (Mallat, 1997). The local frequency characteristics such as the Lipschitz exponents provide some useful information about the oscillation of the spectral curve for each pixel. Different types of materials can be distinguished by the differences in the local frequency variation. The method we propose in this study is called the modulus maxima feature extraction (MMFE) method. In this method, the features are extracted according to the wavelet transform modulus maxima. This new method generates features that are more meaningful and is more stable than other known methods for spectral feature extraction. The fingerprints of spectral curve, the derivative analysis and the wavelet transform are also referred to as multiscale feature extraction because they can emphasize local spectral features in the scale-space plane from course to fine scale
2. Multiscale Feature Extraction Methods
Generally speaking, a feature is any attribute that can be extracted from the measurement data. Features may be numerical, symbolic, or both. For remote sensing data, the molecular absorption bands of water and carbon dioxide cause deep absorption features that complete radiation block transmissions. These spectral regions were avoided for traditional earth surface remote sensing (Schowengerdt, 1997). However, hyperspectral data produces laboratory-like curves with spectral resolution sufficient to describe the essential absorption features of many materials. This spectral analysis characteristic has also renewed interest in extracting physical spectral features in contrast to statistical approaches. One of the earliest physical feature extraction specifications for hyperspectral data was the calculation of image "residual" spectra for mineral detection and identification (Schowengerdt, 1997). This method emphasizes the absorption bands of different minerals relative to an average signature without absorption features. Multiscale methods are used to extract spectral features from course to fine scales. Thus the physical meaning of a spectral curve can be surveyed at different scales. A method of symbolic description called absorption band fingerprints for hyperspectral data was developed by Piech and Piech (1987,1989). The fingerprints are a representation based on a scale space filter for the hyperspectral data. In this method, a scale space image is a set of progressively smoothed
versions produced by convoluting the original spectral curve with a LoG filter. As the smoothing scale increase, features of the curve disappear until only a dominant spectral shape remains. A plot of the points of inflection within the scale space image results in a fingerprint. The net result of the scale space analysis of a hyperspectral data curve is a sequence of triplets. Each triplet describes a spectral feature and contains important measures directly related to the area contained within the spectral feature and the left and right inflection points of the spectral feature. Another method proposed to reduce the effects of atmospheric scattering and absorption on spectral signatures is derivative analysis. The derivatives are estimated using a finite divided difference approximation algorithm with a finite band separation,
Dl=
li+1-
li (Tsai and Philpot, 1997). The derivatives not only emphasize subtle spectral details, but also minimize illumination and atmospheric effects. Thus, derivatives are well suited to extract spectral features relating to specified target properties. A common disadvantage of this method is its extreme sensitivity to noise. For this reason, the derivative computation is typically coupled with spectral smoothing (Tsai and Philpot, 1999).
In this study , the wavelet transform was applied to extract physical features. The wavelet transform can focus on localized signal structures with a zooming procedure. The local frequency characteristics, such as the Lipschitz exponents, provide useful information about the oscillation of the spectral curve for each pixel. In the next section, we briefly introduce the basic theory of wavelet transform and then explain the MMFE method theory.
