||Spectral Feature Extraction of Hyperspectral Images using Wavelet Transform
||Department of Geomatics
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. However, the classification methods that have been successfully applied to multispectral data in the past are not as effective as for hyperspectral data. The main problem is that the training data set does not increase corresponding to the increase of dimensionality of hyperspectral data. Actually, the problem of the “curse of dimensionality” emerges when a statistical classification method applied to 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. The goal of feature extraction is to reduce the number of dimensionality substantially without sacrificing useful information. In this study, several methods based on the wavelet transforms are developed to extract useful features for classification. Firstly, wavelet or wavelet packet transforms are implemented on the hyperspectral images and a sequence of wavelet coefficients is produced. Then, a simple feature selection procedure associated with a criterion is used to select the effective features for classification. Because the wavelet-based feature extraction optimizes the criterion in a lower dimensional space, the problems of limited training sample size and the curse of dimensionality can be avoided. On the other hand, the laboratory-like spectral curves also describe diagnostic absorption and reflection features which are valuable to understand the physical or chemical properties of materials. The other objective of this study is to propose an automatic procedure for the detection of absorption features. By the zooming procedure of continuous wavelet transform (CWT), these localized structures of absorption features can be accurately characterized. While the position of an individual absorption feature is determined, the continuum removal algorithm can be implemented to reduce some additive effects, such as level changes and slopes due to other absorbing or emitting materials. Consequently the parameters of a single absorption feature can be calculated for spectral matching or material identification. Finally, two AVIRIS data sets are used to test the performance of the proposed wavelet-based methods. The experiment results show that the wavelet-based methods perform well for dimensionality reduction and also be effective for classification.
中 文 摘 要 I
LIST OF FIGURES VII
LIST OF TABLES X
CHAPTER 1 INTRODUCTION - 1 -
1.1 IMAGING SPECTROMETERS - 1 -
1.2 MOTIVATIONS - 4 -
1.3 RESEARCH OBJECTIVES - 6 -
1.4 THESIS ORGANIZATION - 7 -
CHAPTER 2 PROPERTIES OF HYPERSPECTRAL IMAGES - 9 -
2.1 INTRODUCTION - 9 -
2.2 CHEMICAL AND PHYSICAL PROPERTIES - 10 -
2.2.1 Absorption Bands - 10 -
2.2.2 Atmospheric Correction - 14 -
2.2.3 Summary - 17 -
2.3 STATISTICAL AND GEOMETRICAL PROPERTIES - 18 -
2.3.1 Spectral Signatures and Distributions - 18 -
2.3.2 Basic Statistics of Distributions - 21 -
2.3.3 Geometric Properties in High-Dimensional Space - 23 -
2.3.4 Summary - 26 -
2.4 CURSE OF DIMENSIONALITY - 27 -
2.4.1 Statistical Pattern Recognition - 27 -
2.4.2 Curse of Dimensionality - 28 -
2.4.3 Summary - 30 -
2.5 VISUALIZATION OF HYPERSPECTRAL IMAGES - 31 -
2.5.1 Introduction - 31 -
2.5.2 Spatial-Spectral Space - 32 -
2.5.3 Spectral Space - 33 -
2.5.4 Scatter Plots - 36 -
2.5.5 Parallel Coordinates - 39 -
2.5.6 Statistics Images - 41 -
2.5.7 Symbolic Representation - 43 -
CHAPTER 3 DIMENSIONALITY REDUCTION OF HYPERSPECTERAL IMAGE - 45 -
3.1 INTRODUCTION - 45 -
3.2 FEATURE SELECTION - 46 -
3.2.1 Criterion Function - 47 -
3.2.2 Optimal Search Procedure - 48 -
3.2.3 Suboptimal Search Procedure - 51 -
3.2.4 Experiments - 53 -
3.3 FEATURE EXTRACTION - 54 -
3.3.1 The Definition of Features - 55 -
3.3.2 Ideal Features for Classification - 56 -
3.4 FEATURE EXTRACTION ALGORITHM OVERVIEW - 57 -
3.4.1 Principal Components Analysis - 58 -
3.4.2 Linear Discriminant Analysis - 59 -
3.4.3 Decision Boundary Feature Extraction Algorithm - 62 -
3.5 EXPERIMENTS - 63 -
3.5.1 Experiment I - 63 -
3.5.2 Experiment II - 67 -
3.6 SUMMARY - 72 -
CHAPTER 4 WAVELET-BASED FEATURE EXTRACTION - 73 -
4.1 INTRODUCTION - 73 -
4.2 FOURIER-BASED FEATURE EXTRACTION - 74 -
4.3 WAVELET-BASED FEATURE EXTRACTION - 77 -
4.3.1 Wavelet Transform - 77 -
4.3.2 Fast Orthogonal Wavelet Transform - 80 -
4.3.3 Linear Wavelet Feature Extraction - 82 -
4.3.4 Experiment I - 88 -
4.3.5 Non-linear Wavelet Feature Extraction - 91 -
4.3.6 Best-Basis Feature Extraction - 94 -
4.3.7 Local Discriminant Basis Feature Extraction - 100 -
4.4 EXPERIMENTS - 103 -
4.4.1 Experiment I - 103 -
4.4.2 Experiment II - 112 -
4.5 SUMMARY - 114 -
CHAPTER 5 ABSOPRTION FEATURE DETECTION OF HYPERSPECTRAL IMAGES - 116 -
5.1 INTRODUCTION - 116 -
5.2 ABSORPTION FEATURE EXTRACTION - 117 -
5.2.1 Definition of Absorption Features - 117 -
5.2.2 Continuum Removal of Absorption Features - 118 -
5.2.3 Summary of Methods for Absorption Features Extraction - 120 -
5.2.4 Fingerprints - 121 -
5.3 WAVELET-BASED FEATURE EXTRACTION - 123 -
5.3.1 Continuous Wavelet Transform - 123 -
5.3.2 Absorption Feature Detection using Modulus Maxima Wavelet Transform - 124 -
5.4 EXPERIMENTS - 133 -
5.4.1 Chlorophyll Absorption Detection - 133 -
5.4.2 Absorption Information Image - 135 -
5.5 SUMMARY - 136 -
CHAPTER 6 CONCLUSION - 138 -
6.1 Summary - 138 -
6.2 SuggestIONs for Further Work - 140 -
BIBLIOGRAPHY - 142 -
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