frequency, It was pointed out in the paper that the method requires 
that one of the images should be restored.  Ehlers (1982) tested 
matching accuracy by applying different filters to homogenous satellite 
imagery with low Signal-to-noise ratio (S/N). The results Show an 
increase in matching accuracy when one of the images is preprocessed by 
Suitable low pass filters, 
In optical and electrical Science, image/signal restoration is well 
known and well developed. Early work in digital image restoration Was, 
for the most part, based on those early developed methods (linear 
methods). This work Will be based on those basic digital image re- 
Storation methods, The investigation has been performed as a 
literature Survey of methods for image restoration. 
2. BASIC DEFINITIONS 
2.1 Linear System 
A system is defined mathematically as a unique transformation or 
operator (Fig 2.1) that maps an input sequence f into an output 
Sequence g (Oppenheim, 1975). Let L define a linear operator, If gq = 
L(£4) and g» - L(£2) then the system is linear if and only if 
Leaf, + b£9) z aL(£4) + bL(£2) = ag; + bg, 
for arbitrary constants a and b. A linear operator (or function) is 
said to be shift invariant or position invariant when its effect on a 
point does not depend on the position of the point in the image i.e. 
L(£(t-)32.2 d(t-x) for all x 
2.2 Convolution 
Shift invariant operations can be carried out either directly in the 
Original spatial domain of the image or in the frequency domain. In 
the first case, any linear shift invariant operation can be expressed 
as the convolution of two functions i.e, 
g(x) = [ f(x)h(x-t)dt (2-1) 
or 
g=£f%h 
where f(x) is the input function of the system, h(x-t) the linear 
operator and g(x) the output of the system. If £(x) is the original 
undistorted image and g(x) the distorted output image then h(x-t) is 
the point-spread-function (psf) of the System, The psf can be ex- 
pressed as a general function of both x and t: 
g(x) - f£GOh(x,t)dt (2-2) 
This equation, known as a Fredholm integral with a two-dimensional 
kernel, is a general description of a linear system in which the 
operator h(x,t) maps an object f(x) into an image g(x), If the 
operator h(x,t) is shift variant the shape of the operator changes as a 
function of its position. If, however, the operator h maintains its 
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