The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
4. If new XV is close enough to XV + , output the vector 
XV .Otherwise, go back to step2. 
3. MULTIRESOLUTION DATA FUSION BSAED ON 
ICA 
The different bands in remote sensing imagery have strong 
correlated, which is caused by some interference factors such as 
weather, atmosphere condition, etc. On other hand, the 
established models for ground object imaging have no enough 
refutation accuracy under some uncertain disturbed conditions. 
So we use ICA to remove the interference, and get an 
independent representation of original bands. Then the high 
frequency information extracted by discrete wavelet transform. 
Considering the high frequency of the image is compared to 
detail part and the low frequency is corresponding to the profile 
part of the image roughly. In our method, the high frequency 
elements in every scale are replaced by the corresponding part 
of the panchromatic frequency bands. Then, reconstruction is 
performed for three multispectral band and we get finally fusion 
result by inversing ICA transform. The diagram on the whole 
process can be found in Fig 1. 
Fig.l the fusion diagram 
In detail, three multispectral bands are firstly changed into three 
vectors R, G, B. Then the fast ICA algorithm mentioned above 
is employed to get three independent components, IC1, IC2, 
IC3. In formula 9, F means an ICA operation. 
Thirdly, the discrete wavelet decomposition is applied on the 
panchromatic band P and three independent components. As 
mentioned in the section 1, only part of wavelet base can be 
used in the fusion procedures to avoid or reduce the artefacts. In 
our experiments, Coiflet bases with different orders, which have 
a. original image b. synthesized P band 
(512x512) (512x512) 
Fig.2 Landsat-P synthesized from three Bl, B2, B3 as 
P = (Bl+B2+B3)/3 
a. 1 multispectral image 
(128x128) 
b.panchromatic band 
(512x512) 
Fig 3 Quick bird image used for fusion 
linear phrase is compared. This procedure can be expressed as 
follow formula 10, 11. 
/ci = 2>,' cl +^C+Z^ cl +V 
;=1 i=l i=l 
/C2 = X*/ C2 + £a; c2 + £ h'f 2 +aJ CI (10) 
/=1 /=1 ;=1 
IC3 = ±hr + £hr+£K ci + aJ 
/=1 1=1 /=1 
/J =2X + ÏX+ÎX+ i C öd 
IC 3 
/•=1 
¿=1 
/•=1 
Where, n is the number of decomposition levels. In the above 
equations, hf, h v p , and hf represent the detail images of the 
PAN image at successively higher scales n, while a„ p is the 
approximation image. The detail and approximation images of 
the IC1,IC2, and IC3 images can be understood similarly. 
Because panchromatic band is rich in spatial information, and 
structure spatial is mainly concentrated on wavelet planes. A 
substitute fusing algorithm can be deduced, (as shown in 
formula 12.)Finally, fusion result can be got by inverse ICA 
transform (In formula 13).