The International Archives oj the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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By this relationship, g(V) must be chosen so that its derivative 
approximately forms a probability distribution function for the 
sources to be recovered. The only remaining parameters to 
adapt are the synaptic weights that can be found by maximizing 
H(Z) with respect to B. The weight update rule will then be a 
gradient descent in the direction of maximum joint entropy. 
More computationally efficient approaches have been proposed 
in (Lee et al., 2000), the reader can obtain more of the 
mathematical details in (Chitroub et al., 2006). If we define the 
term score function as: 
^(v) = fep(v)/dv)/p(v) (7) 
then an efficient weight update is: 
AB cc (|-^(v).V 7 )b (8) 
The form of q(y) plays a crucial role because it is function of 
the transfer and therefore a function of the source estimate. For 
the sub-Gaussian sources, the form of ^v) is such as: 
(/Ay) = V - tanUy) (9) 
where tanh(.) is the hyperbolic tangent. For the super-Gaussian 
sources, (p(y) takes the form: 
(p{y) = v + tanhiy) (10) 
The switching between the sub-Gaussian and super-Gaussian 
learning rule gives the following learning rule for the ICA - 
part model (Lee et al., 1999): 
AB oc (l - K.tanh(v).v T - v.v r )b (11) 
^ is a A-dimensional diagonal matrix with elements 
sigrifuiyi)) • ib(v,) is the kurtosis of the source estimate v,. The 
switching parameter fo(v.) can be derived from the general 
stability analysis of separating solutions (Cardoso, 1996; 
Hyvarinen, 1999). 3 
3. EXPERIMENTAL RESULTS 
We present in this section our preliminary results. More 
detailed study and more completed results are under 
development. They will be subject of the future works for 
publication. A real multi-temporal data provided by the 
Landsat-TM are used to evaluate the proposed method. The 
data were acquired over the AlQassim region in Saudi Arabia 
(140x235pixels) during April and June 1994. The fifth bands of 
the two sets of data are shown in Figure 4. The first three 
extracted PC images are given in Figure 4. The first 
components have the best image quality (contrast). Figure 5 
shows the extracted IC images. These images are different to 
the PC images. In the PC images the correlation is vanished and 
consequently the redundant information is minimized. In these 
images the zones of vegetation temporal evolution stability are 
well mapped since they are characterized by the variance of the 
PC image. This variance is maximized in the first PC images. 
While the contrast between the input spectral images, which 
characterize the differences between the spectral bands, is 
mapped the last PC images that are much noised and 
consequently it is not possible to overcome the information 
about the natural changes undergone by the observed scene. 
However, in IC images the mutual information between the PC 
images are minimized and so the natural changes, which can be 
considered as the mutual information between the transition 
zones of the PC images, are emerged. In the IC images, the 
zones of vegetation temporal evolution stability are also 
preserved as they are in PC images. This can be quantified by 
computing the image of the vegetation stability zones and the 
image of the vegetation transition zones (natural changes) of the 
scene both from the first and the second extracted IC images 
(Figure 6). 
4. CONCLUSION 
In this paper, we have presented a new method for seasonal 
vegetation analysis. The method is based on the emergent 
technique, which is the independent component analysis (ICA). 
The basic idea is to consider that the natural change undergone 
by the observed scene can be detected and emerged if the 
mutual information that exists between the images is minimized. 
This task can be realised by the compound neural network 
model PCA-ICA. We have presented here the main outlines of 
the theoretical analysis of such model. More complicated 
mathematical development of the proposed method cannot be 
given here and it will be subject of the future works for 
publication. Although the preliminary results, given in this 
paper, needed to be evaluated by an objective and mathematical 
criteria, they are, however, of interesting in the sense that the 
extracted IC images are very informative about the surface state 
of the observed scene, concerning the stability and transition 
zones of the vegetation, compared to the extracted PC images. 
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