Because condition (23) depends on image spectral density functions, which 
are not known apriori, the more practical case is considered now for which: 
O(f1f2) -G, for all fj4f9 (27) 
For this suboptimum condition, still applying Wiener filtering i.e. HP =, 
it follows for the rate distortion function: 
72. 2 2 
= 
R (d,) = [frase “log ALLE ap af (28) 
Tfx "Ua 
a = Jf min [te 6 )uen* & (Py Jaf, (29) 
From (28) and (29) it follows that: 
dp = din for P = 1 (30) 
Evaluation results 
The rate distortion function expressed by (28) and (29) has been evaluated 
for the case of P = 1, corresponding to an optimum (Wiener) pre-filter for 
which dr = Armin and for the case H=1, corresponding to an optimum 
(Wiener) post-filter. 
  
The ground reflectivity signal r(x,y) with power a2 is modelled according 
to a two dimensional first-order Gaussian-Markov source, characterized by 
its power spectral density function: 
  
. 4-8. o-m 8 
Sb Cos IO ET A (ff) cn 
for -i,-if,,f2 « i, 
where Px and Py denote respectively the correlation coefficient for the x 
and the y coordinates. 
The SAR pre-processor is fully characterized by the Kaiser-window 
weighting function with cut-off frequencies at |fc1| - [f£ca|= } and the 
number of looks (L). 
Other parameters used in the evaluation are: 
(mem) 
Or 
no 
Yr 
  
as a measure of source dynamics 
^ 
dr as a measure of the relative distortion contribution 
"s z— Of the encoding and filter operations, where with (29), 
dr, the speckle-induced distortion component dm, is given by: 
VES 
dy, = d, («9 [flt e J ad df, (32) 
= 
5» 
450 
  
lon 6 AR & 
r3 CO t Rec OQ) Kk3 €) C MO 4 
EM E 1 er M pu Se (CD C2 €) rn 
NY 
Cat