scale 2” (Mallat, 1999). Because of sub-sampling, the length
of the original signal is reduced after applying conjugate mirror
filer to the original signal. With these properties, wavelet
decomposition is implemented on dimensionality reduction of
hyperspectral images (Hsu, 2003).
Linear and nonlinear wavelet-based feature extraction (WFE)
methods are applied to hyperspectral images in this study. In
linear WFE, the approximation coefficients a; are regarded as
features for classification. On the other hand, nonlinear WFE
consider approximation coefficient a; as well as detail
coefficient d; and select M largest wavelet coefficients as
important features for classification (Hsu, 2003). In the
experiments, the wavelet function used in linear and nonlinear
WFE is Daubechies 3 wavelet (Daubechies wavelet with 3
vanishing moments). The experiment procedure of wavelet-
based feature extraction is illustrated in Figure 2.
3.3 HHT-Based Feature Extraction
According to the characteristics of time-frequency analysis of
HHT, the HHT will be applied to spectral curves of each pixel
in hyperspectral image. First of all, Hilbert-Huang transform is
implemented on a spectral curve. The instantaneous frequency
and amplitude of each component will be calculated. Then Hil-
bert spectrum is formed by using instantaneous frequency and
amplitude. The residual information is also considered in this
spectrum. After that, the M largest values in the Hilbert spec-
trum are selected as the important features of the spectral curve
for classification. These features are sorted by the bands where
the feature is located. If more than two features have same loca-
tion of bands, sort the features according to their frequency. Fi-
nally, the extracted features are used as the inputs for classifica-
tion. Maximum likelihood classifier is used in this study. The
procedure of feature extraction using Hilbert-Huang transform
is illustrated in Figure 2 as well.
N-dimensional
Hyperspectral
Image
Feature Extraction Wavelet Transform
/ Hilbert-Huang Transform
'
;
de Feature T !
1
1
:
En Feature Selection :
xx
Au
Training Data
Training
v
Classification
(Maximum Likelihood Classification)
Figure 2. The flow chart of wavelet-based or HHT-based
feature extraction
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
4. EXPERIMENTS
There are three experiments in this study. The first experiment
is to compare the performance between unsupervised and su-
pervised HHT-based feature extraction. The second experiment
is to compare different WFE methods. Finally, the HHT-based
feature extraction methods are compared with wavelet-based
feature extraction methods mentioned in section 3.2 and 3.3.
4.1 Experiment I: Comparison of Classification Results
between Unsupervised and Supervised HHT-Based
Feature Extraction Methods
The purpose of the experiment is to test the performance of un-
supervised HHT-based feature extraction method. In addition,
the features of supervised HHT-based feature extraction are se-
lected by computing Bhattacharyya distances from the features
extracted by unsupervised HHT-based methods. The classifica-
tion accuracies are calculated for various numbers of features by
HHT-based methods.
Figure 3 shows the classification accuracies with different
HHT-based feature extraction methods. We can find that both
unsupervised and supervised HHT-based methods have good
classification accuracies. The classification results both
conform to Hughes phenomenon that accuracy increases at first
and then accuracy decline when the number of features
increases with constant number of training samples. Compared
with unsupervised HHT-based method, supervised HHT-based
method can improve classification accuracy apparently.
Supervised HHT-based feature extraction can achieve better
classification accuracy (90%) with six and seven features,
whereas unsupervised HHT-based method has lower accuracy
(81.33%) with four features. Therefore, supervised HHT-based
method can have better results by calculating the separability of
different classes with training samples than unsupervised HHT-
based method.
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Figure 3. Comparison of classification accuracies between
HHT-based methods
