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As these results show, the intensities of the neighboring pixels 
are very strongly correlated in the image channels; just a single 
added band is required for the handling of neighborhood. This 
last possibility isn't the theme of current paper; it points for 
future works. 
This unbelievable strong correlation can also be proved by the 
visualization of the correlation matrix. Case of 4-neighborhood 
is presented in Figure 5a, the 8-neighborhood in Figure 5b. The 
periodicity isn't too difficult to detect in both cases. 
     
  
   
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b) 8-neighborhood 
Figure 5. Visualization of the correlation coefficients’ absolute 
values in all bands with neighborhood extension 
  
  
  
  
  
Figure 6. Coefficients plot for a single band (values are shown 
with their absolute values) 
Barsi, Arpad 
Plotting the absolute values of correlation coefficients of just a 
single band (e.g. Band 7), this relation is more visual. (Figure 6) 
The relation can’t be measured too well with the linear 
correlation coefficient but the analysis is noticable! (The 
periodicity could be proven even better by such plots.) 
The analysis of the test set brings the same results about close 
relations. 
If the visualization of the neighboring pixels are completed 
band by band, the relations between the bands are much bright: 
see Figure 7 in the 4-neighborhood case! 
  
Figure 7. The relation between the pixels in the 4-neighborhood 
(band by band visualization) 
The figure above illustrates well, that Band 4 and Band 6 are the 
differing image channels, while the others are strongly 
correlated. It’s supposed that the Karhunen-Loeve 
transformation is calculated with the majority of these bands. 
(The tools of mathematical factor analysis could answer this 
question and prove this hypothesis.) 
3. RESULTS 
3.1. Neural network for the original image 
The presented effective Levenberg-Marquard training method 
calculated the network parameter changes, so the training 
process was fast. Only some epochs (iterations) were necessary 
to reach the desired error goal level. The initial goal level was 
0.01, which produced 4 errors (0.2 96) for all training data. 
Setting the value to 0.005, in 17 epochs a totally error-free 
network is designed. The training is shown in Figure 8. 
    
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Figure 8. Training the neural network for the original data set 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 143