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the fiber - optic distributed measuring systems were being actively developed during the past few years @xcite . particularly these systems can be used for acoustic field investigating , for monitoring of stresses in industry , in geophysical researches , etc .
the reconstruction of information obtained by measuring system needs solving of tomographic problem .
but frequently such solution is complex , needs large computer consumption and can not be performed in real time .
therefore previously learned neural network can be utilized for solving of tomographic problem @xcite .
an optical perceptron , which was implemented using a collection of amplitude holograms recorded on a disk - shaped holographic carrier and processing the output data from a fiber - optic measuring system , is reported in ref .
another computer linear neural network was developed by authors of refs .
we present the similar computer non - linear feed - forward neural network in this paper .
consider two - dimensional fiber - optic distributed measuring system being set of measuring lines .
the fiber - optic phase sensors form square @xmath0 lattice also having @xmath1 diagonal lines ( fig .
[ square ] ) .
the phase shift @xmath2 in this linear sensor is proportional to physical action value integrated over the line while the intensity of the transmitted light @xmath3 .
the phase shift in fiber - optic line have to be along one cosine half - period .
signal from such measuring system is simulated on input of neural network which is intended to reconstruct the value of physical action at intersection points .
the @xmath4 fiber - optic distributed measuring system . ]    for solving of tomographic problem we choose perceptron with the non - linear hidden layer since this network has universal approximation capability @xcite .
the neurons of the first layer serve as network inputs and feed data from the measuring system to the next layer .
the second ( hidden ) layer proceeds following transformation : @xmath5 where @xmath6 are states of neuron inputs being signals from measuring sensors , @xmath7 are states of outputs and @xmath8 are synapses .
we used @xmath9 as activation function @xmath10 .
the hidden layer of neurons has @xmath11 inputs and @xmath0 outputs .
the output layer of the neurons takes the linear transformation : @xmath12 where @xmath13 are states of third layer neuron outputs , @xmath14 are synapses of third layer .
we selected gaussian distributions of the some physical quantity with one or two peaks as learning patterns .
the following expression was used as objective function : @xmath15 where @xmath16 is superscript indicating number of learning pattern , @xmath17 are output states of the neural network for some learning pattern . for the training pattern @xmath6
are formed as squared cosines of the sum of @xmath17 along the corresponding measuring line .
we used error back - propagation for the network training , so we had to minimize @xmath18 with respect to @xmath8 , @xmath14 .
we combined conjugate gradient and coordinate descent minimization methods for neural network learning .
when conjugate gradient method failed we switched to the coordinate descent and after some iterations tried to start conjugate gradient minimization again .
also we applied the `` thermal jumps '' technique .
the minimization procedure finished after certain iteration count or on given accuracy reaching .
on the first step we learned the neural networks to reconstruct the signal having , as well as training patterns , one gaussian peak .
examples of initially unknown reconstructed distributions with different variances and @xmath19 are shown in tables [ example - delta ] , [ example - smooth ] .
the neural networks was learned independently in all the cases with the similar randomly generated patterns .    on the next step we trained neural networks reconstructing distributions with two gaussian peaks .
examples are shown in the tables [ example - delta2 ] , [ example - smooth2 ] . in the case of the smooth distribution
the reconstructed signal is close to the original . for the @xmath20-like distributions the locations of the peaks
are recovered correctly but their magnitude differs from the original .
one can see from tables that neural network sufficiently accurately reconstructs unknown pattern and can be used in practice
.    presented neural network unlike refs .
@xcite can work not only with signal from fiber - optic measuring line being within the interval of linear dependence of light intensity on phase shift .
the computer model of the neural network solving tomographic problem is proposed .
this network can be used in conjunction with the distributed fiber - optic measuring system and partly may be made as electronic or optical hardware .
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a computer model of the feed - forward neural network with the hidden layer is developed to reconstruct physical field investigated by the fiber - optic measuring system . 
 the gaussian distributions of some physical quantity are selected as learning patterns . 
 neural network is learned by error back - propagation using the conjugate gradient and coordinate descent minimization of deviation . 
 learned neural network reconstructs the two - dimensional scalar physical field with distribution having one or two gaussian peaks .    
 * keywords : * neural networks , optical tomography , fiber - optic measuring systems