)-
bod
IS
2.3 Comparisons between Wavelet Transform and Hilbert-
Huang Transform
Wavelet transform and Hilbert-Huang transform are both time-
frequency analysis tools, so that they can analysis the variation
of data in both time and frequency domain. Table 1 shows some
differences between wavelet transform and HHT. Firstly,
wavelet transform have complete theoretical base and have to
define a basis function before using it; whereas, HHT with
empirical theoretical base has an adaptive basis, which can
analysis data adaptively. Second, wavelet transform computes
frequency by convolution operation; while, the frequency is
derived by differentiation rather than convolution in HHT.
However, wavelet transform and HHT can present the results in
time-frequency-energy space. Finally, wavelet transform is
suitable for nonstationary data but is unsuitable for nonlinear
data. On the contrary, HHT is suitable for both nonlinear and
nonstationary data. Therefore, HHT is a superior tool for time-
frequency analysis of nonlinear and nonstationary data (Huang,
2005).
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
Wavelet Transform HHT
Theoretical Base Theory complete Empirical
Basis A prior Adaptive
Frequency Convolution Differentiation
Pros État Energy-time- Energy-time-
frequency frequency
Nonlinear Data Unsuitable Suitable
Nonstitionay Suitable Suitable
Data
Table 1. Comparisons between Wavelet and Hilbert-Huang
Transform (Huang, 2005)
3. HYPERSPECTRAL IMAGE FEATURE
EXTRACTION
3.1 Datasets Description
In this study, an AVIRIS data set is used to test the performance
of using wavelet transform and HHT on hyperspectral image
feature extraction and classification. The AVIRIS data set
shown in Figure 1(a) is the well-known Cuprite data set, which
is a mineral region at Nevada. The image size of the test field is
350x350. The number of bands is 224. Figure 1(b) also shows a
mineral map produced in 1995 by USGS. In this study, we
choose 6 classes from this map (Table 2) for feature extraction
and classification. Table 2 also shows the number of training
samples and check sample for image classification.
# of training # of check
Class names
samples samples
Alunite 100 50
Kaolinite 100 50
Muscovite 100 50
Calcite 100 50
Montmorillonite 100 50
Kaolinite-- i
ao me Semectite or 100 50
uscovıte
Table 2. The 6 chosen classes
Cuprite, Nevada
AVIRIS 1995 Data
| USGS
Clark & Swayze
Tricorder 3.3 product
E K-Alunite 150C
K-Alunite 250C
K-Alunite 450C
Na82-Alunite 100C
Na40-Alunite 400C
Kaolinite wx1
2 Kaolinite px!
Kaolinite+smectite
cr muscovite
Montmorillonite
alcite +Kaolinite
a
* Montmorillonite
~ low-Al muscovite
ed-Al muscovite
gh-Al muscovite
arosite
uddingtonite
=A Chalcedony
Nontronite
Pyrophyllite
+ alunite
Chlorite +
lontmorillonite
or Muscovite
Chlorite
(b) Mineral map in Cuprite(USGS Spectroscopy Lab, 1998)
Figure 1. An AVIRIS data set of Cuprite
3.2 Wavelet-Based Feature Extraction
The orthogonal wavelet transform can decompose a signal into
the low-frequency components that represent the optimal
approximation, and the high-frequency components that
represent detailed information of the original signal (Mallat,
1989). The decomposition coefficients in a wavelet orthogonal
basis can be computed with a fast algorithm that cascades
discrete convolutions with conjugate mirror filters (CMF) h and
g, and subsamples the outputs. The decomposition equations
are described as following:
a, [pl=) hin-2pla [n]
gn (10)
j*l
d,,[p]= S gIn- 2p]a [n]
n=-0
a; is the approximation coefficients at scale 2, and aj, and dj.;
are respectively the approximation and detail components at
