<s>
In	O
electrical	O
engineering	O
and	O
applied	O
mathematics	O
,	O
blind	B-Algorithm
deconvolution	I-Algorithm
is	O
deconvolution	B-Algorithm
without	O
explicit	O
knowledge	O
of	O
the	O
impulse	O
response	O
function	O
used	O
in	O
the	O
convolution	B-Language
.	O
</s>
<s>
Blind	B-Algorithm
deconvolution	I-Algorithm
is	O
not	O
solvable	O
without	O
making	O
assumptions	O
on	O
input	O
and	O
impulse	O
response	O
.	O
</s>
<s>
However	O
,	O
blind	B-Algorithm
deconvolution	I-Algorithm
remains	O
a	O
very	O
challenging	O
non-convex	O
optimization	O
problem	O
even	O
with	O
this	O
assumption	O
.	O
</s>
<s>
In	O
image	B-Algorithm
processing	I-Algorithm
,	O
blind	B-Algorithm
deconvolution	I-Algorithm
is	O
a	O
deconvolution	B-Algorithm
technique	O
that	O
permits	O
recovery	O
of	O
the	O
target	O
scene	O
from	O
a	O
single	O
or	O
set	O
of	O
"	O
blurred	O
"	O
images	O
in	O
the	O
presence	O
of	O
a	O
poorly	O
determined	O
or	O
unknown	O
point	O
spread	O
function	O
(	O
PSF	O
)	O
.	O
</s>
<s>
Regular	O
linear	O
and	O
non-linear	O
deconvolution	B-Algorithm
techniques	O
utilize	O
a	O
known	O
PSF	O
.	O
</s>
<s>
For	O
blind	B-Algorithm
deconvolution	I-Algorithm
,	O
the	O
PSF	O
is	O
estimated	O
from	O
the	O
image	O
or	O
image	O
set	O
,	O
allowing	O
the	O
deconvolution	B-Algorithm
to	O
be	O
performed	O
.	O
</s>
<s>
Researchers	O
have	O
been	O
studying	O
blind	B-Algorithm
deconvolution	I-Algorithm
methods	O
for	O
several	O
decades	O
,	O
and	O
have	O
approached	O
the	O
problem	O
from	O
different	O
directions	O
.	O
</s>
<s>
Most	O
of	O
the	O
work	O
on	O
blind	B-Algorithm
deconvolution	I-Algorithm
started	O
in	O
early	O
1970s	O
.	O
</s>
<s>
Blind	B-Algorithm
deconvolution	I-Algorithm
is	O
used	O
in	O
astronomical	O
imaging	O
and	O
medical	O
imaging	O
.	O
</s>
<s>
Blind	B-Algorithm
deconvolution	I-Algorithm
can	O
be	O
performed	O
iteratively	O
,	O
whereby	O
each	O
iteration	O
improves	O
the	O
estimation	O
of	O
the	O
PSF	O
and	O
the	O
scene	O
,	O
or	O
non-iteratively	O
,	O
where	O
one	O
application	O
of	O
the	O
algorithm	O
,	O
based	O
on	O
exterior	O
information	O
,	O
extracts	O
the	O
PSF	O
.	O
</s>
<s>
Iterative	O
methods	O
include	O
maximum	B-General_Concept
a	I-General_Concept
posteriori	I-General_Concept
estimation	I-General_Concept
and	O
expectation-maximization	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
Examples	O
of	O
non-iterative	O
techniques	O
include	O
SeDDaRA	O
,	O
the	O
cepstrum	B-Algorithm
transform	O
and	O
APEX	O
.	O
</s>
<s>
The	O
cepstrum	B-Algorithm
transform	O
and	O
APEX	O
methods	O
assume	O
that	O
the	O
PSF	O
has	O
a	O
specific	O
shape	O
,	O
and	O
one	O
must	O
estimate	O
the	O
width	O
of	O
the	O
shape	O
.	O
</s>
<s>
Any	O
blurred	O
image	O
can	O
be	O
given	O
as	O
input	O
to	O
blind	B-Algorithm
deconvolution	I-Algorithm
algorithm	O
,	O
it	O
can	O
deblur	O
the	O
image	O
,	O
but	O
essential	O
condition	O
for	O
working	O
of	O
this	O
algorithm	O
must	O
not	O
be	O
violated	O
as	O
discussed	O
above	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
deconvolution	B-Algorithm
of	O
seismic	O
data	O
,	O
the	O
original	O
unknown	O
signal	O
is	O
made	O
of	O
spikes	O
hence	O
is	O
possible	O
to	O
characterize	O
with	O
sparsity	B-Algorithm
constraints	O
or	O
regularizations	O
such	O
as	O
l1	O
norm/l2	O
norm	O
norm	O
ratios	O
,	O
suggested	O
by	O
W	O
.	O
C	O
.	O
Gray	O
in	O
1978	O
.	O
</s>
<s>
Audio	O
deconvolution	B-Algorithm
(	O
often	O
referred	O
to	O
as	O
dereverberation	O
)	O
is	O
a	O
reverberation	O
reduction	O
in	O
audio	O
mixtures	O
.	O
</s>
<s>
One	O
possibility	O
is	O
to	O
use	O
ICA	B-Algorithm
.	O
</s>
<s>
The	O
channel	O
can	O
usually	O
be	O
modeled	O
as	O
a	O
linear	O
shift-invariant	O
system	O
,	O
so	O
the	O
receptor	O
receives	O
a	O
convolution	B-Language
of	O
the	O
original	O
signal	O
with	O
the	O
impulse	O
response	O
of	O
the	O
channel	O
.	O
</s>
<s>
This	O
system	O
is	O
called	O
an	O
equalizer	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
we	O
can	O
filter	O
the	O
received	O
signal	O
to	O
obtain	O
the	O
desired	O
spectral	B-Algorithm
power	I-Algorithm
density	I-Algorithm
.	O
</s>
<s>
This	O
is	O
what	O
happens	O
,	O
for	O
example	O
,	O
when	O
the	O
original	O
signal	O
is	O
known	O
to	O
have	O
no	O
auto	O
correlation	O
,	O
and	O
we	O
"	O
whiten	B-Algorithm
"	O
the	O
received	O
signal	O
.	O
</s>
<s>
Most	O
blind	B-Algorithm
deconvolution	I-Algorithm
techniques	O
use	O
higher-order	O
statistics	O
of	O
the	O
signals	O
,	O
and	O
permit	O
the	O
correction	O
of	O
such	O
phase	O
distortions	O
.	O
</s>
<s>
We	O
can	O
optimize	O
the	O
equalizer	B-Algorithm
to	O
obtain	O
a	O
signal	O
with	O
a	O
PSF	O
approximating	O
what	O
we	O
know	O
about	O
the	O
original	O
PSF	O
.	O
</s>
<s>
Blind	B-Algorithm
deconvolution	I-Algorithm
algorithms	O
often	O
make	O
use	O
of	O
high-order	O
statistics	O
,	O
with	O
moments	O
higher	O
than	O
two	O
.	O
</s>
