<s>
Super-resolution	B-Algorithm
imaging	I-Algorithm
(	O
SR	O
)	O
is	O
a	O
class	O
of	O
techniques	O
that	O
enhance	O
(	O
increase	O
)	O
the	O
resolution	B-Algorithm
of	O
an	O
imaging	B-Algorithm
system	O
.	O
</s>
<s>
In	O
optical	O
SR	O
the	O
diffraction	O
limit	O
of	O
systems	O
is	O
transcended	O
,	O
while	O
in	O
geometrical	O
SR	O
the	O
resolution	B-Algorithm
of	O
digital	B-Algorithm
imaging	I-Algorithm
sensors	O
is	O
enhanced	O
.	O
</s>
<s>
In	O
some	O
radar	B-Application
and	O
sonar	B-Application
imaging	B-Algorithm
applications	O
(	O
e.g.	O
</s>
<s>
magnetic	O
resonance	O
imaging	B-Algorithm
(	O
MRI	O
)	O
,	O
high-resolution	B-Algorithm
computed	I-Algorithm
tomography	I-Algorithm
)	O
,	O
subspace	O
decomposition-based	O
methods	O
(	O
e.g.	O
</s>
<s>
MUSIC	O
)	O
and	O
compressed	O
sensing-based	O
algorithms	O
(	O
e.g.	O
,	O
SAMV	B-Algorithm
)	O
are	O
employed	O
to	O
achieve	O
SR	O
over	O
standard	O
periodogram	O
algorithm	O
.	O
</s>
<s>
Super-resolution	B-Algorithm
imaging	I-Algorithm
techniques	O
are	O
used	O
in	O
general	O
image	B-Algorithm
processing	I-Algorithm
and	O
in	O
super-resolution	B-Algorithm
microscopy	O
.	O
</s>
<s>
Because	O
some	O
of	O
the	O
ideas	O
surrounding	O
super-resolution	B-Algorithm
raise	O
fundamental	O
issues	O
,	O
there	O
is	O
need	O
at	O
the	O
outset	O
to	O
examine	O
the	O
relevant	O
physical	O
and	O
information-theoretical	O
principles	O
:	O
</s>
<s>
Information	O
:	O
When	O
the	O
term	O
super-resolution	B-Algorithm
is	O
used	O
in	O
techniques	O
of	O
inferring	O
object	O
details	O
from	O
statistical	O
treatment	O
of	O
the	O
image	O
within	O
standard	O
resolution	B-Algorithm
limits	O
,	O
for	O
example	O
,	O
averaging	O
multiple	O
exposures	O
,	O
it	O
involves	O
an	O
exchange	O
of	O
one	O
kind	O
of	O
information	O
(	O
extracting	O
signal	O
from	O
noise	O
)	O
for	O
another	O
(	O
the	O
assumption	O
that	O
the	O
target	O
has	O
remained	O
invariant	O
)	O
.	O
</s>
<s>
Resolution	B-Algorithm
and	O
localization	O
:	O
True	O
resolution	B-Algorithm
involves	O
the	O
distinction	O
of	O
whether	O
a	O
target	O
,	O
e.g.	O
</s>
<s>
The	O
word	O
ultra-resolution	O
had	O
been	O
proposed	O
for	O
this	O
process	O
but	O
it	O
did	O
not	O
catch	O
on	O
,	O
and	O
the	O
high-precision	O
localization	O
procedure	O
is	O
typically	O
referred	O
to	O
as	O
super-resolution	B-Algorithm
.	O
</s>
<s>
The	O
technical	O
achievements	O
of	O
enhancing	O
the	O
performance	O
of	O
imaging-forming	O
and	O
–	O
sensing	O
devices	O
now	O
classified	O
as	O
super-resolution	B-Algorithm
utilize	O
to	O
the	O
fullest	O
but	O
always	O
stay	O
within	O
the	O
bounds	O
imposed	O
by	O
the	O
laws	O
of	O
physics	O
and	O
information	O
theory	O
.	O
</s>
<s>
Both	O
would	O
utilize	O
normal	O
passband	O
transmission	O
but	O
are	O
then	O
separately	O
decoded	O
to	O
reconstitute	O
target	O
structure	O
with	O
extended	O
resolution	B-Algorithm
.	O
</s>
<s>
The	O
usual	O
discussion	O
of	O
super-resolution	B-Algorithm
involved	O
conventional	O
imagery	O
of	O
an	O
object	O
by	O
an	O
optical	O
system	O
.	O
</s>
<s>
But	O
modern	O
technology	O
allows	O
probing	O
the	O
electromagnetic	O
disturbance	O
within	O
molecular	O
distances	O
of	O
the	O
source	O
which	O
has	O
superior	O
resolution	B-Algorithm
properties	O
,	O
see	O
also	O
evanescent	O
waves	O
and	O
the	O
development	O
of	O
the	O
new	O
Super	O
lens	O
.	O
</s>
<s>
Known	O
defects	O
in	O
a	O
given	O
imaging	B-Algorithm
situation	O
,	O
such	O
as	O
defocus	O
or	O
aberrations	O
,	O
can	O
sometimes	O
be	O
mitigated	O
in	O
whole	O
or	O
in	O
part	O
by	O
suitable	O
spatial-frequency	O
filtering	O
of	O
even	O
a	O
single	O
image	O
.	O
</s>
<s>
Provided	O
that	O
there	O
is	O
enough	O
light	O
,	O
this	O
can	O
be	O
achieved	O
with	O
arbitrary	O
precision	O
,	O
very	O
much	O
better	O
than	O
pixel	O
width	O
of	O
the	O
detecting	O
apparatus	O
and	O
the	O
resolution	B-Algorithm
limit	O
for	O
the	O
decision	O
of	O
whether	O
the	O
source	O
is	O
single	O
or	O
double	O
.	O
</s>
<s>
This	O
technique	O
,	O
which	O
requires	O
the	O
presupposition	O
that	O
all	O
the	O
light	O
comes	O
from	O
a	O
single	O
source	O
,	O
is	O
at	O
the	O
basis	O
of	O
what	O
has	O
become	O
known	O
as	O
super-resolution	B-Algorithm
microscopy	O
,	O
e.g.	O
</s>
<s>
This	O
can	O
be	O
achieved	O
at	O
separations	O
well	O
below	O
the	O
classical	O
resolution	B-Algorithm
bounds	O
,	O
and	O
requires	O
the	O
prior	O
limitation	O
to	O
the	O
choice	O
"	O
single	O
or	O
double	O
?	O
"	O
</s>
<s>
The	O
approach	O
can	O
take	O
the	O
form	O
of	O
extrapolating	O
the	O
image	O
in	O
the	O
frequency	O
domain	O
,	O
by	O
assuming	O
that	O
the	O
object	O
is	O
an	O
analytic	B-Language
function	I-Language
,	O
and	O
that	O
we	O
can	O
exactly	O
know	O
the	O
function	O
values	O
in	O
some	O
interval	O
.	O
</s>
<s>
This	O
method	O
is	O
severely	O
limited	O
by	O
the	O
ever-present	O
noise	O
in	O
digital	B-Algorithm
imaging	I-Algorithm
systems	O
,	O
but	O
it	O
can	O
work	O
for	O
radar	B-Application
,	O
astronomy	O
,	O
microscopy	O
or	O
magnetic	O
resonance	O
imaging	B-Algorithm
.	O
</s>
<s>
More	O
recently	O
,	O
a	O
fast	O
single	O
image	B-Algorithm
super-resolution	I-Algorithm
algorithm	O
based	O
on	O
a	O
closed-form	O
solution	O
to	O
problems	O
has	O
been	O
proposed	O
and	O
demonstrated	O
to	O
accelerate	O
most	O
of	O
the	O
existing	O
Bayesian	O
super-resolution	B-Algorithm
methods	O
significantly	O
.	O
</s>
<s>
Geometrical	O
SR	O
reconstruction	O
algorithms	O
are	O
possible	O
if	O
and	O
only	O
if	O
the	O
input	O
low	B-Algorithm
resolution	I-Algorithm
images	O
have	O
been	O
under-sampled	O
and	O
therefore	O
contain	O
aliasing	B-Error_Name
.	O
</s>
<s>
Because	O
of	O
this	O
aliasing	B-Error_Name
,	O
the	O
high-frequency	O
content	O
of	O
the	O
desired	O
reconstruction	O
image	O
is	O
embedded	O
in	O
the	O
low-frequency	O
content	O
of	O
each	O
of	O
the	O
observed	O
images	O
.	O
</s>
<s>
if	O
the	O
images	O
of	O
the	O
scene	O
are	O
shifted	O
by	O
a	O
sub-pixel	O
amount	O
)	O
,	O
then	O
the	O
phase	O
information	O
can	O
be	O
used	O
to	O
separate	O
the	O
aliased	O
high-frequency	O
content	O
from	O
the	O
true	O
low-frequency	O
content	O
,	O
and	O
the	O
full-resolution	O
image	O
can	O
be	O
accurately	O
reconstructed	O
.	O
</s>
<s>
shift-add	O
fusion	O
)	O
,	O
the	O
presence	O
of	O
aliasing	B-Error_Name
is	O
still	O
a	O
necessary	O
condition	O
for	O
SR	O
reconstruction	O
.	O
</s>
<s>
There	O
are	O
very	O
both	O
single-frame	O
and	O
multiple-frame	O
variants	O
of	O
SR	O
.	O
Multiple-frame	O
SR	O
uses	O
the	O
sub-pixel	O
shifts	O
between	O
multiple	O
low	B-Algorithm
resolution	I-Algorithm
images	O
of	O
the	O
same	O
scene	O
.	O
</s>
<s>
It	O
creates	O
an	O
improved	O
resolution	B-Algorithm
image	O
fusing	O
information	O
from	O
all	O
low	B-Algorithm
resolution	I-Algorithm
images	O
,	O
and	O
the	O
created	O
higher	O
resolution	B-Algorithm
images	O
are	O
better	O
descriptions	O
of	O
the	O
scene	O
.	O
</s>
<s>
These	O
methods	O
use	O
other	O
parts	O
of	O
the	O
low	B-Algorithm
resolution	I-Algorithm
images	O
,	O
or	O
other	O
unrelated	O
images	O
,	O
to	O
guess	O
what	O
the	O
high-resolution	B-Algorithm
image	O
should	O
look	O
like	O
.	O
</s>
<s>
Originally	O
,	O
super-resolution	B-Algorithm
methods	O
worked	O
well	O
only	O
on	O
grayscale	O
images	O
,	O
but	O
researchers	O
have	O
found	O
methods	O
to	O
adapt	O
them	O
to	O
color	O
camera	O
images	O
.	O
</s>
<s>
Recently	O
,	O
the	O
use	O
of	O
super-resolution	B-Algorithm
for	O
3D	O
data	O
has	O
also	O
been	O
shown	O
.	O
</s>
<s>
There	O
is	O
promising	O
research	O
on	O
using	O
deep	B-Architecture
convolutional	I-Architecture
networks	I-Architecture
to	O
perform	O
super-resolution	B-Algorithm
.	O
</s>
