56 
P' = A(P) 
P' = I>,+A 
i 
comparisons. A Pair of LANDSAT Thematic Mapper (TM) and 
SPOT images are also evaluated (size256 X 256),in order to 
test whether the merging method of this paper extend to actual 
PAN and MS images. 
Where, i is the number of decomposition levels and W i is the 
responding wavelet plane. P r is the remaining approximation 
part. 
Because panchromatic band is rich in spatial information, and 
structure spatial is mainly concentrated on wavelet planes. An 
additive fusing algorithm can be deduced. It can be easy to 
conclude that the wavelet planes are ranged from fine and 
coarse, when the scale rises. And we need to extract finer detail 
of PAN to Mulspectral bands, so a descent weight array A is 
used to moderate different plane W. . (as shown in formula 
12.)Finally, fusion result can be got by inverse ICA transform 
(In formula 13). 
/c; = X^ (+ /c, 
i=l 
C 2 = ^ J A i w i + IC 2 ( 12 ) 
j=i 
c;=5>, + /c 3 
¿=1 
[«', G\ B'] = F' (ic;, IC[ ,/C 3 ') (13) 
4. EXPERIMENTAL RESULTS AND COMPARISONS 
4.1 Synthetic Datasets and Real MS-PAN Datasets 
The main aim of this research is to determine the efficiency of 
new algorithm based on ICA for merging images with a 
particular resolution ratio. Due to the difficulties in obtaining 
adequate imagery with particular ration, Yocky’s approach [9] is 
employed to synthesize some MS-PAN datasets with particular 
ratio. In this approach, a Landsat TM test image was available 
in the three bands,i.e., B1 (green), B2 (red), and B3 (near 
infrared). The image was used to synthesize a perfectly 
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 
overlapped panchromatic band at 20 m, which is shown in. 
Then, the MS bands were decimated by two and used together 
with the P at 20 m, to synthesize Bl, B2, and B3 back at 20 m. 
there are several reasons to emphasis on the merging of 
simulated Pand decimated multispectral bands. Firstly, all the 
images are spatially coregistered, and any problem caused by 
geometric corrections in fusing process can be avoided. 
Secondly, we can get the true multispectral data for objective 
4.2The Quality Analysis of the Fusion Image 
We have adopted some quantification metrics to evaluate the 
fusion quality, including entropy, mean, and standard 
deviation, Average gradient. Among these metrics, entropy 
explores the information changes, and an image has more 
information when the entropy is bigger. And some other metrics, 
such as mean, employed to evaluate the aberrance of the 
spectral information. The mean calculates the degree of the 
spectral information change. In our research, different 
decomposition levels for Atrous wavelet have been tested. 
The result for data set is show in Fig 3. 
For visual analysis, we could find that our method can enhance 
the image spatial resolution to a certain degree, which will 
benefit those applications which are demanding strictly on the 
details of an image, such as image interpretation, special 
cartography, and photogrammetric survey, etc. With 
decomposition level increasing, more panchromatic band 
a. original MS bands b. 1 level 
c.2 level d.3 level 
Fig3 the fusion result with different decomposition 
levels for synthetic data size(512 X 512) 
information is injected into three multispectral bands and gray 
levels of images become sharper. But on the other hand, the 
spectral distortion became worse. It means that it may be have a 
tradeoff between the spectral and spatial quality. So when we 
must consider about the decomposition parameter by combining 
with the post-processing purpose. We have also adopted some 
quantification metrics to evaluate the fusion quality. The 
statistical data is shown in table 1. It can be included from tables: 
the information in both of the two datasets is increased in the 
case of the injection of the information .Because the high 
frequency information in the multispectral bands is substituted 
selectively by the corresponding parts in the panchromatic band. 
So we proposed an useful fusing algorithm. 
Metrics 
Band 
Original 
spectral 
1 2 
3 
R 
bands 
149.73 
149.99 149.88 
145.93 
Mean 
G 
138.87 
139.01 139.12 
139.23 
B 
116.28 
115.92 115.75 
118.49 
Standard G 
deviation g 
R 
Average G 
gradient g 
R 
Entropy G 
B 
Tabled statis 
5.COr 
A new multispectr 
provided by comb 
The experiment re 
spatial informatioi 
spectral distortion 
future, our work 
fusion rule for infc 
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