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)
=
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