a) 
Cc) 
  
Fig 3.1 Image degradation model. a) original image, 
b) original deblurred by a Gaussian psf, c) random noise, 
d) deblurred plus random noise 
field at the position r. The autocorrelation of the random field f is 
defined as Rfg(ri,r2) » E(r4r2). The random field is said to be 
Stationary (homogenous, invariant) if the mean me(r) is a constant 
independent of its position, and the autocorrelation of the random 
field is independent of its position, varying only as a function of the 
Euclidian distance between ry and rp. The random field is said to he 
ergodic if the ensemble mean is constant and equal to the spatial 
average (time average in one dimension). 
J.1.2 Deterministic Image Model 
In a deterministic image model it is assumed we know the fundamental 
nature of the image. This may be described in parametric or non- 
parametric form. The former requires a functional description of the 
image. This may be achieved by Segmenting the image into primitive 
regions, which can be described functionally as image primitives 
(Andrews and Hunt, 19773. "The nonparametric form can be described by a 
Set of constraints on the image (ex nonnegative grey levels). 
3.2 Image Degradation Model 
Normally, most analysis models for image processing systems are 
formulated under the assumptions that these systems have a linear pst 
(Andrews, 1975). A common degradation process may then be modelled by 
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