signal and measured data
because of the instrumental inexelence

??measured datas differs from true signal.
The presence of the noise is one of the main factors that 
make the restoration of true signal difficult


how the symmetry of the equation that describe 
the procces of data formation can be used to eliminate the noise.


WHERE THIS PROBLEM OCCUR
different kind of telescopy image proccessing, electrophoresis,


HOW IT MAY BE MATHEMATICALY FORMULATED
Finite resolution -> discrete data sets
Values of the true signal emmited from points of a certain 
object are stored in one set and observed datas in the second set of the 
same size.
 
because of measurement procces 
the true signal from each single point of the object is spreeded to 
different points in the data set.

Mathematicaly this bluring can be described by the equation

B=K*O
in which O is diagonal matrix with entries equal to the values of the signal
K is the matrix that describe spreed, 


from each point of the object can reach 
different points in the set of
datas


Without the noise the set O and D 

of points
object and observed datas are represented by sets of points.

signal from each point of the object can reach different points in the set of
datas

true value of the signal in each point of the 
signal from each point of the object can reach different points in the set of
datas



how the spred appears
true signal array 
Spreed array 
Spreeded signal Array

noise array
how the noise appears


SPRED AND NOISE discussion -> question of solvability

Spreed array can be calibrated, tested, and is known with
some accuracy, ussualy gaussian core and and so on

Known about 

noise unknown it is ussualy only assumed to posses certain mean value and 
distribution.


disadvantages of existing methods

filtering is a compromise beetwen removing the noise and damaging true 
signal.
The fitting yields only aproximation, which may be far from the signal 
(and may contain undesirable artifacts)


SYMMETRY - additional information about the signal