Attributes 
Harr 
Daubechies 
BiorSplines 
Coiflets 
Symlets 
Morlet 
Orthogonality 
Yes 
Yes 
No 
Yes 
Yes 
Yes 
The tighten 
support length 
1 
2N-1 
2N+1 
6N-1 
2N-1 
00 
Filter length 
2 
2N 
2N+2 
6N 
2N 
[-4,4] 
Symmetry 
Symmetry 
Symmetry 
approximatively 
Asymmetry 
Symmetry 
approximatively 
Symmetry 
approximatively 
No 
Vanishing 
moment 
1 
N 
N-l 
2N 
2N 
- 
Table. 1 Attributes of the different wavelet bases 
Form the table 1, the filter length of Haar wavelet is 2. The 
filter length makes a great effect on the image fusion. The 
shorter the filter length is, the more the target information loses. 
In the case of the same filter length, the great vanishing 
moment will lead to the smaller wavelet coefficients that may 
be ignored under detailed scale, and makes the detail of the 
image blurry. Symmetry can reconstruct the image well. 
Therefore, Daubechies wavelet is chosen to integrate the SAR 
and optical images in the paper. 
3. DAUBECHIES WAVELET LIFTING TRANSFORM 
expressed as: 
fh(z) = h 0 + l\z 1 + h 2 z 2 + h i z 3 
[ g(z) = -h^z 2 + h 2 z — 1\+ h 0 z~ ] 
(l) 
Where 
/2 0 = (1 + v/3 ) / 4 V2,/tj = (3 + V3 ) / 4 v/2 
h 2 = (3 - v/3 ) / 4, h 3 = (1 - V3 ) / 4V2 
The wavelet lifting technique has widely been applied. The 
lifting wavelet presents the under trait: calculating in the same 
location, manifesting the high efficiency, calculating in the 
parallel means, constructing easily and transforming by integer 
[4 l Usually, the lifting wavelet may be constructed with two 
kinds of the ways. On the one hand the traditional wavelet may 
be implemented by the lifting scheme means, on the other hand 
the new wavelet may directly be constructed using the lifting 
means. 
For the Daubechies D4, the function of the filter may be 
To decompose the multiphase matrix, the under equation may 
be obtained: 
’i S' 
1 0' 
1 z 
(V3+l)/V2 0 
0 1 
ß/4+(S-2)/4z-' 1 
0 1 
0 (V3-l)/V2_ 
(2) 
Step 
The transform forward 
The transform backward 
Step 1 
s (0) = X 
¿k A 2k 
4 2) =Cd t 
Step 2 
d T = X 1M 
4 2) = s t /( 
Step 3 
4™-d«»+«(,«■>+,{«) 
4'>=^fw£)-4 2> 
Step 4 
sT=s^+ß(d^ + d^) 
^ ,, = r(4 1, +4‘- , l )-4 2> 
Step 5 
4«>=A4 1, +^i)-4 1) 
Step 6 
4 0) =«(4 0) +4°-l)-4 1> 
Step 7 
* t = c4 2> 
1 = 4 0) 
Step 8 
x u= st t >) 
Table.2 The Lifting process of the Daubechies wavelet