bul 2004 
—— 
e object 
ject and 
ructure., 
undancy 
pectrum 
  
Landsat 
imaging 
age 
  
41 
46 
31 
  
1€ same 
pectrum 
nd these 
he band 
in this 
ression. 
different 
s design 
, the 2D 
textured 
are high 
elet can 
ly. This 
in high 
wavelet 
alyse to 
wavelet 
efers to 
[lowing 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
® Consistent monotony 
MS Mon 
@ Gradually perfectibility 
n-0.UV,-LG o 
mez 
I^ Cru. (1) 
Q Regulation of flex 
fo)eyp,e/fQxep vmezo 
Riesze there is 
Ve 
@  Existency of base: 
pel’, 
And ge V. 
eX x-n),neZz as theRiesze base of 
can meet the following condition: 
  
V,^spanie(x-n)nez (9 
< < < © 
Á A; which can obtain the 
(CHE 
Thus, there is 
following arbitrary relation to 
AX|ci | X con) s c4 
neZ nez” 
T 
(5) 
where presents the square summary of total list, that is: 
[ou (ar). 2 al 2m (6) 
(2) Construction of Multi-band wavelet 
As the multi-scale analyse, the scale function with interposition 
property can be constructed and corresponding conjugated 
filtering of M-band as the following equation: 
5 
M 
[=z [+6 
+ 
M 4-7) 2 2 
  
H(z)= 
  
(7) 
Thus, the wavelet coefficient can be obtained through the above 
equation. 
(3) Image multi-band decompose and reconstruct 
As the above scale function and the , we can obtain the image 
wavelet decomposition and reconstruction algorithm. 
; a T 
Taken image as ^ ^2 ^. the wavelet decomposition formula 
of M-band wavelet can be expressed as following: 
HJ = NS _MkCn, —MI uA M (8) 
My M, 
57 
  
=0,/<s, <M—! 
22 Cd Mk n, S ut nm 5 
Ye. Mk n, — E uin 3 ys 
Ye. Mk CA ny —A m jun, uS 
The corresponding image reconstruct to the M-band wavelet 
can be expressed as: 
p Se Ci-Mn, aur 
mn Ma 
SS C on Ci-un, T + 
Jh Hy 
bh + 
z0/ss,sM-lI 
M-1 
>, Nw. Mn, dr. Mn, D. 
s,.$2=0,5,+s2=0 | M 
M-l 
NE 3,555 ) 
dq Mn, LÆ k-Mn, D. 
Sp S2 m0, s ess m 
(10) 
2.3 Edge Reservation based Quantification Algorithm in 
Multi-band Wavelet Domain 
After multi-band wavelet transformation, the images are 
divided into different parts. The compression based on wavelet 
generally adopt different quantification methods to different 
wavelet coefficient. The 2D wavelet transformation can obtain 
the edge image while the edge image size is one of 2* of the 
original image size. The multi-band wavelet can obtain edge 
image with arbitrary size and can well keep the image structure 
and edge feature. Figure 1 is the low frequency edge coefficient 
images of 3D wavelet decomposition. 
Figure 1 3D Wavelet Decomposition 
The general quantification of the high frequency wavelet 
coefficient is the same. As figure shown, the high frequency 
coefficient of multispectrum image after wavelet transformation 
preserves the texture structure and edge feature in different 
directions. If the coefficient present the edge, the wavelet 
coefficient is high. And the plain region in the image has low 
wavelet coefficient. In order to keep the object edge and 
contour, the quantification of wavelet coefficient with edge and 
contour should adopt high and precise level while the plain 
region can be quantize with coarse level. In this paper, the 
wavelet coefficient quantification is done after the edge 
extraction. Hence the edge is detected from the high frequency 
wavelet coefficient, the left wavelet coefficient can be 
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