<s>
The	O
generalized	B-Algorithm
Wiener	I-Algorithm
filter	I-Algorithm
generalizes	O
the	O
same	O
idea	O
beyond	O
the	O
domain	O
of	O
one-dimensional	O
time-ordered	O
signal	O
processing	O
,	O
with	O
two-dimensional	O
image	B-Algorithm
processing	I-Algorithm
being	O
the	O
most	O
common	O
application	O
.	O
</s>
<s>
The	O
generalized	B-Algorithm
Wiener	I-Algorithm
Filter	I-Algorithm
is	O
the	O
linear	B-Architecture
operator	I-Architecture
which	O
minimizes	O
the	O
expected	O
residual	O
between	O
the	O
estimated	O
signal	O
and	O
the	O
true	O
signal	O
,	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
Gaussian	O
distributed	O
signal	O
and	O
noise	O
,	O
this	O
estimator	O
is	O
also	O
the	O
maximum	B-General_Concept
a	I-General_Concept
posteriori	I-General_Concept
estimator	I-General_Concept
.	O
</s>
<s>
The	O
generalized	B-Algorithm
Wiener	I-Algorithm
filter	I-Algorithm
approaches	O
1	O
for	O
signal-dominated	O
parts	O
of	O
the	O
data	O
,	O
and	O
S/N	O
for	O
noise-dominated	O
parts	O
.	O
</s>
<s>
In	O
this	O
formulation	O
,	O
the	O
generalized	B-Algorithm
Wiener	I-Algorithm
filter	I-Algorithm
becomes	O
using	O
the	O
identity	O
.	O
</s>
<s>
The	O
generalized	B-Algorithm
Wiener	I-Algorithm
filter	I-Algorithm
exploits	O
this	O
difference	O
in	O
behavior	O
to	O
isolate	O
as	O
much	O
as	O
possible	O
of	O
the	O
signal	O
from	O
the	O
noise	O
.	O
</s>
<s>
The	O
solution	O
must	O
in	O
these	O
cases	O
be	O
found	O
by	O
solving	O
the	O
equivalent	O
equation	O
,	O
for	O
example	O
via	O
conjugate	B-Algorithm
gradients	I-Algorithm
iteration	O
.	O
</s>
