2.4 Determination of spectral components 
Let’s discuss methods of obtaining information 
about optical picture making use of neuron networks. 
Envisage some neuron network with nonlinear 
interconnections. Assume that optical signal 
influences on each neuronlike element. Besides, 
magnitude of electrical signal in network is enough 
that nonlinearity would be able to reveal itself. 
Suppose that only part of all quantity of elements 
are lighted up.This group located at the begining of 
network.Another part of neurons have no influence of 
light and connected with lighted section only 
electrically.Such example one can find in /9/.There 
non linearity is realized using capacity. After 
exposition a set of solitins forms along the network 
and besides of this there appears a component of 
continuous spectrum. After a while solitons, moving 
along the network, reach to its darked part.And 
continuous component forms as linear interaction 
between neurons.Hence it distributes along whole 
line, decreasing own amplitude.Consequently we can 
suggest that main part of information contains in 
solitons which move with different velocities.Center 
of soliton is at 
: nt 
x = § -c (qt 
where B; - const 
Its Velorıly is equal to C(- n°) .More strong soliton 
moves quicker than weak one. 
With the aid of neuron system it is possible to 
devide weak solitons which correspond to high 
frequency spectrum part from strong ones which 
characterize low frequency components of spectrum. 
All discussed solitons have different velocities. 
Hence at the darked end of network strong pulses 
appear earlier. One can offer method of 
soliton characteristics determination.Most important 
are amplitude and width.But they have one-to-one 
correspondence. 
Let’s find derivative of signal with respect to 
time for two neibouring neurons and compare moments 
when y = 0. This procedure enables to get time 
interval between apparence of solitons at first and 
second neurons.Beometrical distance one can choose 
taking into account information about brightness of 
source and its extent.Thus at darked end of network 
all solitons are identified sequently. 
Becouse we envisage situation when process has 
become settled, it is possible to realize 
identification by control soliton which moves to 
meet information ones.It can be recieved from other 
networks as well.During collision of two solitons 
they acquare phase shifts which depend on components 
of discrete spectrum corresponding to them. 
Furthemore, these phase shifts may be stated as 
following relation 
ou Loo "ts S = + Lo Nat Na 
Go) 5, d gel AM se 
Introduce additional function 
F = arctan (e I) 
After collision due to phase shifts function F 
suffers jump, characterizing by big value of time 
derivative.Counting up all those jumps along network 
and knowing in advance amplitude of control soliton, 
set of discrete components are determined without 
fails. 
Besides, signal measurement in a single network 
the same operation is possible using information, 
containing in several networks. Imagine two 
identical networks, for example, two neighbour ones. 
  
20 
First, light distribution at every of them is 
identical too. Let us fix two pairs of neurons at 
each network with the same number. And choose those 
pairs at a short distance. Begin to calculate 
function F using signals from every pair for this 
operation. If illuminances are identical as supposed 
above, then we will obtain as a result F = 45 in 
every moment. The same signal will be observed at 
the next output, connected with the next pair. 
Examination of pair with another number, different 
from those, shows that there are not change of 
initial picture. This result shows as well 
coincidence of signals at both networks. 
Imagine situation when at the second network 
initial picture has small differences from first 
one. Then , as we have seen above, discrete spectrum 
will suffer changes too. Several solitons will 
increase or decrease their amplitudes and 
accordingly their velocities. That pair of neurons 
which number is the least, will acquire 
insignificant change. The more number of next pair 
is different from initial one, the more function F 
acquires change. It can be explained by different 
coordinates of two corresponding solitons in some 
moment. It is advisable to introduce such parameter 
as length of identity. It can be defined taking into 
consideration permissible level of difference F from 
au", 
Üne and the same 2 D network can have different 
discrete spectrum structure depending on topology of 
all subnetworks. Calculation of function F will 
enable to produce optimal topology. Choose minimum 
of equivalent length as a criterion of identity. In 
that situation discrete spectrum is most rich. Let 
us place several pairs of neurons for measurement of 
Fat 2D photodetector plane. And envisage several 
standart  topologies to choose optimal type. This 
task was solved for 12x12 matrix with the aid of 
digital computer. It Was examined following 
types of possible networks : horizontal lines, 
vertical lines, rectangulars and spirals. For 
different light distribution optimal topology should 
be determined. 
Algorithm, represented above, evidently is 
suboptimal one, because we examined only standart 
types of networks. More complex task is to form 
network by changing this network through several 
steps, leading criterion to minimum. 
Several values, corresponding to discrete 
spectrum, characterize received optical signal, its 
parameters.Comparison with the standart image will 
enable to estimate difference in their spectrums.If 
it is necessary one can rehabilitate initial image 
making use the method of inverse scattering 
transform (/10/), 
2.5 Signal distortion 
Special question of influence of different 
distortions of initial image on discrete spectrum 
components should be discussed. Assume that light 
distribution at the detector plane suffered a small 
increment 5 yGO. Then after substitution of it into 
Schredinger equation and making some transformations 
we get 2 
Gy gars ES f$) v Zoe 
Hence increments of discrete spectrum component 
depend on type of optical signal, i.e. how many 
elements there are in the series corresponding to 
this signal. Coefficients Yk are time independent. 
In other situations it is possible to correct 
initial signal with the aid of spectral correction. 
mn 
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