<s>
The	O
Richardson	B-Algorithm
–	I-Algorithm
Lucy	I-Algorithm
algorithm	I-Algorithm
,	O
also	O
known	O
as	O
Lucy	O
–	O
Richardson	O
deconvolution	B-Algorithm
,	O
is	O
an	O
iterative	B-Algorithm
procedure	I-Algorithm
for	O
recovering	O
an	O
underlying	O
image	O
that	O
has	O
been	O
blurred	B-Language
by	O
a	O
known	O
point	O
spread	O
function	O
.	O
</s>
<s>
When	O
an	O
image	O
is	O
produced	O
using	O
an	O
optical	O
system	O
and	O
detected	O
using	O
photographic	O
film	O
or	O
a	O
charge-coupled	B-Algorithm
device	I-Algorithm
,	O
for	O
instance	O
,	O
it	O
is	O
inevitably	O
blurred	B-Language
,	O
with	O
an	O
ideal	O
point	O
source	O
not	O
appearing	O
as	O
a	O
point	O
but	O
being	O
spread	O
out	O
into	O
what	O
is	O
known	O
as	O
the	O
point	O
spread	O
function	O
.	O
</s>
<s>
In	O
that	O
case	O
the	O
above	O
equation	O
becomes	O
a	O
convolution	B-Language
.	O
</s>
<s>
So	O
a	O
two	O
dimensional	O
detected	O
image	O
is	O
a	O
convolution	B-Language
of	O
the	O
underlying	O
image	O
with	O
a	O
two	O
dimensional	O
point	O
spread	O
function	O
plus	O
added	O
detection	O
noise	O
.	O
</s>
<s>
In	O
order	O
to	O
estimate	O
given	O
the	O
observed	O
and	O
a	O
known	O
,	O
the	O
following	O
iterative	B-Algorithm
procedure	I-Algorithm
is	O
employed	O
in	O
which	O
the	O
estimate	O
of	O
(	O
called	O
)	O
for	O
iteration	O
number	O
t	O
is	O
updated	O
as	O
follows	O
:	O
</s>
<s>
Writing	O
this	O
more	O
generally	O
for	O
two	O
(	O
or	O
more	O
)	O
dimensions	O
in	O
terms	O
of	O
convolution	B-Language
with	O
a	O
point	O
spread	O
function	O
P	O
:	O
</s>
<s>
where	O
the	O
division	O
and	O
multiplication	O
are	O
element	O
wise	O
,	O
indicates	O
a	O
2D	O
convolution	B-Language
,	O
and	O
is	O
the	O
flipped	O
point	O
spread	O
function	O
.	O
</s>
<s>
In	O
problems	O
where	O
the	O
point	O
spread	O
function	O
is	O
not	O
known	O
a	O
priori	O
,	O
a	O
modification	O
of	O
the	O
Richardson	B-Algorithm
–	I-Algorithm
Lucy	I-Algorithm
algorithm	I-Algorithm
has	O
been	O
proposed	O
,	O
in	O
order	O
to	O
accomplish	O
blind	B-Algorithm
deconvolution	I-Algorithm
.	O
</s>
