4.3 Signal-dependent and -independent Nojse 
For the purpose of analysis, noise can be divided into two categories: 
Signal-dependent and -independent. These two can be described with an 
additive and a multiplicative model for the image formation. The noise 
is normally treated as additive. In this case the image intensity 
distribution is described by: 
gíx,y) = f(x,y) + n(x,y) (4.3) 
where n(x,y) describes the noise term. This model is a good rep- 
resentation of noise from the electronic components in a digitizing 
system and for the effects of quantization noise from the Analogue to 
Digital conversion. 
The grain noise is signal-dependent ( Manual of Remote Sensing, 1983 ) 
A better description of image formation than ( 4.3 ) is: 
g(x,y) fix,y) + fix,y) n, ( 4.4 ] 
or 
f(x,yMl 1 * n. 1] s f(x,y) n ( 4.5.) 
gix,y) 1 2 
where n, and n, are random coefficients. 
One way to treat this kind of noise is to take the logarithm of 
expression ( 4.5 ): 
log g(x,y) = log f(x,y) + log n, {°4:6 3 
Another approach is to determine the worst-case noise and allow for it 
using an additive model. 
5. A M FOR THE Y NG PR 
When an image is digitized the intensity distribution represented by 
it is sampled at a set of discrete points. This process can be divided 
and analyzed in two steps. The sampling in space will be considered in 
this section while the grey level quantization will be treated in the 
following one. 
5.1 igitizing wj a Finite e 
When modelling the digitizing process, it is natural to consider the 
image as a two-dimensional signal, f(x,y), reprensenting the grey 
level at the point (x,y). In a real system the digitizing is done with 
a finite aperture ( Whal, 1984 ). This corresponds to a convolution of 
the signal with an aperture function a(x,y): 
4 (x,y) = Fix,y) = aix.y) (3.1) 
The sampling is represented by multiplication with a set of 
dirac pulses and this is written: 
f”(x,y) = f'(x,y) I I ölx-mäöx,y-n Ay) (5.2 à 
ms-e pnz-e 
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