possibilities. For instance if Q - I (unit matrix) the solution leads 
to a general inverse filter (HTH + vI)~1HT (Bjerhammar, 1973) called 
pseudoinverse. Applying the filter to the degraded image g gives the 
pseudoinverse restored image. If the original image f is known to be à 
smooth function the criterion could be to minimize the second order 
derivatives of f. Such a criterion would require that the ohject 
estimate does not oscillate too wildly (Andrews and Hunt, 19773. 
4.4 Geometric Mean Filter 
Suppose it is desirable to de-emphasize the low frequency domination of 
the Wiener filter while avoiding the early singularity of the inverse 
filter. That may he performed by a parameterization of the ratio of 
the inverse filter to Wiener filter (Andrews and Hunt, 19772). Using 
the Fourier approach one such parameterization might yield an estimate 
of the object as follows 
F(s) = (N(2)2 W(=)172) Gls) (4-19) 
where 0 <= a <= 1 and where the linear filter (N& w1-8) is composed of 
the inverse filter component N(s) and the Wiener filter component W(s) 
having the forms 
N(s) = _ H(s)* 
abs(H(s))2 
  
and 
H(s)* 
abs(H(s))2 + V Py(s)/P£(S) 
Wis) 
  
For V=1 and with "a" varying from 0 to 1 the filter changes 
continuously from the original Wiener filter to an jdeal inverse 
filter. This filter represents a general class of restoration filters 
applicable in cases involving linear, Space invariant psf and 
stationary random £ield image models. 
5. DISCUSSION 
5.1 Nonstationary Image Restoration 
The filters based on statistical models discussed in the previous 
sections all assumed a stationary random field model. For an image to 
be stationary, the locally computed power spectrum (the Fourier 
transform of the autocorrelation function) would have to be 
approximately equal over the entire image (Castleman, 1979). This 
condition of position invariant must also pe fulfilled for local means. 
These conditions are seldom satisfied £or aerial photos. Such images 
may be modelled as a collection of homogenous regions separated by 
boundaries with relatively high gradient. Many noise sources, £ilm- 
grain noise for example, cannot be considered as stationary random 
fields (Castleman, 1979), Hunt (1981) proposes the following method to 
process nonstationary images: The image is transformed into a new image 
which can be described by a stationary random £ield model. This new 
image can then be processed by a stationary model algorithm and finally 
inverse transformed into the nonstationary mode. Even though the 
images seldom are stationary in a global meaning, they may be 
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