<s>
In	O
mathematics	O
,	O
Wiener	B-Algorithm
deconvolution	I-Algorithm
is	O
an	O
application	O
of	O
the	O
Wiener	O
filter	O
to	O
the	O
noise	O
problems	O
inherent	O
in	O
deconvolution	B-Algorithm
.	O
</s>
<s>
It	O
works	O
in	O
the	O
frequency	O
domain	O
,	O
attempting	O
to	O
minimize	O
the	O
impact	O
of	O
deconvolved	B-Algorithm
noise	O
at	O
frequencies	O
which	O
have	O
a	O
poor	O
signal-to-noise	O
ratio	O
.	O
</s>
<s>
The	O
Wiener	B-Algorithm
deconvolution	I-Algorithm
method	O
has	O
widespread	O
use	O
in	O
image	O
deconvolution	B-Algorithm
applications	O
,	O
as	O
the	O
frequency	O
spectrum	O
of	O
most	O
visual	O
images	O
is	O
fairly	O
well	O
behaved	O
and	O
may	O
be	O
estimated	O
easily	O
.	O
</s>
<s>
Wiener	B-Algorithm
deconvolution	I-Algorithm
is	O
named	O
after	O
Norbert	O
Wiener	O
.	O
</s>
<s>
where	O
denotes	O
convolution	B-Language
and	O
:	O
</s>
<s>
The	O
Wiener	B-Algorithm
deconvolution	I-Algorithm
filter	O
provides	O
such	O
a	O
.	O
</s>
<s>
and	O
are	O
the	O
Fourier	B-Algorithm
transforms	I-Algorithm
of	O
and	O
,	O
</s>
<s>
,	O
,	O
and	O
are	O
the	O
Fourier	B-Algorithm
transforms	I-Algorithm
of	O
,	O
and	O
,	O
and	O
,	O
respectively	O
,	O
</s>
<s>
and	O
then	O
performing	O
an	O
inverse	O
Fourier	B-Algorithm
transform	I-Algorithm
on	O
to	O
obtain	O
.	O
</s>
<s>
As	O
mentioned	O
above	O
,	O
we	O
want	O
to	O
produce	O
an	O
estimate	O
of	O
the	O
original	O
signal	O
that	O
minimizes	O
the	O
mean	B-Algorithm
square	I-Algorithm
error	I-Algorithm
,	O
which	O
may	O
be	O
expressed	O
:	O
</s>
<s>
The	O
equivalence	O
to	O
the	O
previous	O
definition	O
of	O
,	O
can	O
be	O
derived	O
using	O
Plancherel	O
theorem	O
or	O
Parseval	O
's	O
theorem	O
for	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
.	O
</s>
