The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
components concentrating detail information of original image. 
We note original image f(x,y) as L , and the 3-level two- 
dimension discrete wavelet decomposition of image is shown as 
Figure.1. 
Ü 
Hi 
Hi 
Hi 
Hi 
Hi 
Hi 
Hi 
H\ 
Hi 
H—high-frequent 
component 
L—low-frequent 
component 
superscript 1,2,3— 
decomposition level 
subscript 1.2,3— 
direction number 
Figure. 1 The 3-level two-dimension discrete wavelet 
destruction of image 
In traditional fusion method based on wavelet transform, detail 
component of multispectral image is substituted by detail 
component of panchromatic image in frequent domain, and then 
fused image is obtained by reconstruction of wavelet 
coefficients of multispectral image. Let P, X and F are 
panchromatic image, multispectral image, and fused image, 
respectively. The process of fusion based on wavelet transform 
is as follows: 
1. After the strictly registration and other pre-processing of P 
and X images, the J-level two dimension discrete wavelet 
decomposition are done for the two images respectively, 
and the pyramid images of P and X images, noted as P'"”' 
and X pym respectively, are obtained, containing the 
corresponding low-frequent approximate components and 
high-frequent detail components. 
2. The detail component of X pym is substituted by that of 
P p>m , and the low-frequent approximate component of 
X Pym is preserved, then the fused pyramid image F pym is 
obtained. Therefore, F pym is consists of the detail 
components of P pym and the approximate component of 
ypym 3 
3. The fused image F is obtained by reconstructing and 
reverse transforming the fused pyramid image F pym . 
In traditional fusion methods based on wavelet transform, due 
to the directly abnegation of low-frequent approximate 
component of panchromatic image, the detail information of 
panchromatic image lose in some sense. Fortunately, many 
advanced methods have proposed (Li, 1994), but they nearly 
preserves information of original images in the application- 
oriented aspect. Consequently, traditional fusion methods based 
... normal / , W S X >y)- W k> 
w k (X,y) = L 
W. -W. 
(4) 
on wavelet transform still eclectically preserve spatial detail 
information and spectral information. 
3. AUTO-ADAPTIVE INFORMATION 
PRESERVATION FUSION METHOD BASED ON 
WAVELET TRANSFORM 
The idea of the novel fusion method regards SAR image as 
main body, aiming to preserving information of SAR image 
better, and performing the fusion according to auto-adaptive 
information preservation. The algorithm is as follows: 
1. A window of n><n, (n=3,5,...JT) is defined. Let S is SAR 
image, Xis multispectral image, and k=\,2,...,K represents 
the band sequence of multispectral image. The entropies of 
S and each band of X in the window are calculated. 
* 
In/' (1) 
i=0 
H k (x,y) = -'£ p u \n p tl (2) 
i=0 
where, i = 0,1,.../ is digital number (DN), (x, y) is 
position of the central-pixel in the window, P. and P k are 
ratios of the i pixel number to the total pixel number in the 
window for SAR image and multispectral image, 
respectively. 
2. The discrepancy of information capacity between SAR 
image and the Ath band of multispectral image is expressed 
by the weight W k (jc, y) : 
W k (x,y) = H s ( x ,y) IH k (x,y) (3) 
3. The window is employed to move and perform the same 
operation of 1-2 steps, and the circulation does not cease 
until the entire image is covered at all. And a new weight 
image of the Ath band W k is accomplished. Hence, all of 
K weight images corresponding to K bands of multispectral 
image are gained. 
4. The normalization of weight images is done to limit 
W k (x, y) between 0 and 1: 
where, W™™“ 1 (*, _y) i s the normalization of W k (x, y) , 
W. and W. . are the maximum and minimum of 
A max k mm 
W k (x, y) , respectively. 
5. The J-level two dimension discrete wavelet decomposition 
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