ibul 2004 International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
' wavelet In order to minimize the residue Rx, g is chosen to maximize absorption bands and short-wave infrared region. There are 10 
70 * ^4 5s " ~ 
s the best such that known classes of different vegetation type and one class of 
(x.2.,) water in this test field. The mean spectra of each class are 
shown in Figure 6. The results of various feature extraction 
method are fed to the Maximum Likelihood classifier (MLC) to 
  
g, = arg max (x.g, ) (11) test the classification effectiveness of the extracted features. 
dex that e T 
a signal. 
tation for 
for signal In each of the consecutive steps, the vector g, €D is matched 
problems. 
posed by 
basis for 
nction D 
a known 
can be a 
Then a 
istinguish Figure 4. An AVIRIS data set of Jasper Ridge Biological 
form the Summing (12) from m between 0 and M-1 yields Preserve 
criminant 
'Trgence is Tier osos Beoicgai Forsarve. Veystebon Carwresets 
M-I zu i 
criminant i * (13) 
; X= R X, 0 )g, +R x 
le in the >( Sy, [er 
children 
criminant 
keep the 
best basis 
sures are energy conservation. 
we don’t 
criminant 
; : : } : 
to the residual R"x, which is the m^ order residue left after 
subtracting results of previous iterations: 
RA SR AR CE (12) 
  
m=0 
The orthogonality of A"*'x and g in each iteration implies 
  
  
  
I? = See, pe 04 
m=0 
Figure 5. Jasper Ridge Vegetation Map (© JRPB, Copyright 
“TION 1996, Stanford University) 
sed on the 
intervals exponentially to 0 when m tends to infinity (Mallat, 1999). A 
s can be matching pursuit can be implemented with a fast algorithm that 
the signal (Rx, g,) is calculated from (R"x,g,) ? 
different i i ny 
le case of : en 
cket basis T 
he set of (R™'x,g,) = {Zs g,) or (R"x, Ey. Xe, , M (15) 
r then the tes 
prove the FE ew 
gorithms Finally, the M vectors (g, l,,,, Chosen to minimize the Figure 6. The mean spectra of 11 different classes 
1e vectors = i 
;, with no 
One may prove that the residue |=" will converge 5 Lh. 
a IF 
  
residues at each iteration are directly used as the features for 
; ea Figure7 illustrates the classification results of the extracted 
hyperspectral image classification. 
features using the wavelet-based and matching pursuit feature 
extraction methods. In this experiment, the classification 
nd Zhung accuracies arc calculated for various numbers of features 
for signal 4 „EXPERIMENTS extracted by different wavelet-based methods. We summarized 
ry one by the results of this experiment in the following. Firstly, as the 
is closely number of features increase, the accuracies of classification 
Fricditum terms of classification accuracy. Figure 4 shows the AVIRIS increase in the beginning and then decrease. The results 
n. In this dataset tested in this experiment which is available in the conform to the Hughes phenomenon. Secondly, the results of 
orithm to AVIRIS Wehsite of NASA JPL nonlinear wavelet-based methods including the matching 
ation. Let pursuit, best basis algorithm and LDB methods have the similar 
V vectors, results which are better than the results of linear WFE and PCT 
methods. The basic concept of linear WFE is similar to the PCT 
methods. They are based on the same criterion that the best 
approximation with the minimum error is used as a set of 
important features. The experiment results show that the 
features extracted by these two methods almost have the 
identical effectiveness. Thirdly, when the number of features is 
The main purpose of this experiment is to compare the wavelet- 
based feature extraction methods described in this paper in 
(http://popo.jpl.nasa.gov/html/aviris. freedata.html). This image 
Was acquired in 1996 and covered the Jasper Ridge Biological 
ing x on à Preserve of Stanford University. Figure 5 shows the vegetation 
Map corresponding to the test field. The image size of the test 
field is 180x200. The radiance spectra have been corrected to 
Surface reflectance. From the original 224 spectral channels, 98 
Spectral bands corresponding to the visible and near-infrared 
(10) regions are used in this test, discarding the atmospheric 
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