108 
Table 2 shows the process of the decomposition and 
reconstruction of the Daubechies wavelet using the lifting 
ways. 
4. THE SAR IMAGE AND OPTICAL IMAGE FUSION 
The image may be decomposed to the low-frequency 
sub-image and high-frequency sub-images by the wavelet 
transform. For the low-frequency sub-image, the main intention 
of the image fusion is to reserve the spectral information of the 
optical image, and restrain the noise of the SAR image as much 
as possible [5] . Usually, the power average method is used to 
integrate the low-frequency sub-images. For the high-frequency 
sub-images, which present the variational characteristics of the 
targets, the image fusion may be handled using the different 
fusion operators in term of the application. The fusion operator 
is the keys to integrate the high-frequency sub-images. 
4.1 The rule for the low-frequency image fusion 
A view of the influence of the noise in SAR image, the regional 
average method is firstly used to denoise the SAR sub-image 
when integrating the low-frequency sub-images. Then, the 
power average method is used to integrate the SAR image and 
the optical image. 
The low-frequency sub-image of the SAR image is firstly 
transformed using the regional average method: 
WM lhereeionalaverase > 7) 
Then, the SAR image and the optical image are integrated by 
the under fuction: 
W nM .0J) = w 1 ■fr sa (i,j) + Q-w i )-W„(i,J) (3) 
Where 
W, is the power coefficient, and its value is [0,1]. 
4.2 The rule for the high-frequency image fusion 
The purpose of the high-frequency image fusion is to integrate 
the detail information of the images. Because of the 
discontinuity of the SAR high-frequency sub-images, the 
method in the paper focuses on integrating the optical high- 
frequency sub-images in order to keep the integrality of the 
features, which will make a great influence on the reliability of 
the image matching, especially for the real aperture radar image 
matching. So the fusion image should present the SAR image 
characteristics and keep the integrality of the features as much 
as possible. 
On the basis of the analysis of the high-frequency sub-images, 
the ratios of the high-frequency coefficients are calculated 
between horizontal and vertical directions in the windows, 
which are automatically alterable in according with the 
features-size. The noise dots will be detected because the 
energy along the horizontal and vertical directions is 
approximatively equal if the feature is a noise dot. After the 
noise is retained, the method based on the ratio of the variance 
is used to integrate the SAR and optical high-frequency 
sub-images. 
Namely, according to the speckle noise, the windows may be 
automatically changed from 3x3 to 9x9. The higher 
variance in the windows will be regarded as the pixel value of 
the high-frequency sub-images fusion if the feature in the SAR 
sub-images isn’t a noise dot. The equation is followed as: 
W F»,iolU) = 
w 0P (Uj) 
KAU) 
Wsar(U) 
if speckle 
z / ^op — ^SAR 
if <j op < & SAR 
(4) 
Where 
the variance of the window is defined as id is the size of 
the windows): 
<7*(Uj) = , 1 2 X -W k (m + i,n+j)f 
(2£7 "FI) m=-d n=-d 
w o,j)= 1 2 X XXo n +i, n +j) 
yZu + l) m=-d n=-d 
4.3 Integrating the SAR image and optical image 
Because the speckle noise makes a great influence on the 
feature extraction, it is more important to restrain the noise and 
integrate the spectrum and features information of the optical 
image. After the images of the SAR and optical image have 
been registered, the calculation processes of this method follow 
as: 
1) Decomposing respectively the SAR and optical images 
using lifting wavelet technique. Generally, the level is 3. 
2) For the low frequency sub-image fusion, the average 
coefficients based on the power is adopted. In order that the 
image could show the characteristic of the SAR imagery, the 
power value over 0.5 is assigned to the SAR image. For the 
SAR low frequency sub-image of the first level, the 
sub-images will be integrated after SAR sub-image is filtered 
using the regional average ways. 
3) For the high frequency sub-image fusion, the ratios of the 
high-frequency coefficients are firstly calculated between the 
horizontal direction and the vertical one. Then, a new scheme,