<s>
Image	B-Algorithm
noise	I-Algorithm
is	O
random	O
variation	O
of	O
brightness	O
or	O
color	O
information	O
in	O
images	O
,	O
and	O
is	O
usually	O
an	O
aspect	O
of	O
electronic	O
noise	O
.	O
</s>
<s>
It	O
can	O
be	O
produced	O
by	O
the	O
image	B-Algorithm
sensor	I-Algorithm
and	O
circuitry	O
of	O
a	O
scanner	B-Application
or	O
digital	B-Device
camera	I-Device
.	O
</s>
<s>
Image	B-Algorithm
noise	I-Algorithm
can	O
also	O
originate	O
in	O
film	O
grain	O
and	O
in	O
the	O
unavoidable	O
shot	O
noise	O
of	O
an	O
ideal	O
photon	B-Application
detector	O
.	O
</s>
<s>
Image	B-Algorithm
noise	I-Algorithm
is	O
an	O
undesirable	O
by-product	O
of	O
image	O
capture	O
that	O
obscures	O
the	O
desired	O
information	O
.	O
</s>
<s>
Typically	O
the	O
term	O
“	O
image	B-Algorithm
noise	I-Algorithm
”	O
is	O
used	O
to	O
refer	O
to	O
noise	O
in	O
2D	O
images	O
,	O
not	O
3D	O
images	O
.	O
</s>
<s>
Image	B-Algorithm
noise	I-Algorithm
can	O
range	O
from	O
almost	O
imperceptible	O
specks	O
on	O
a	O
digital	O
photograph	O
taken	O
in	O
good	O
light	O
,	O
to	O
optical	O
and	O
radioastronomical	O
images	O
that	O
are	O
almost	O
entirely	O
noise	O
,	O
from	O
which	O
a	O
small	O
amount	O
of	O
information	O
can	O
be	O
derived	O
by	O
sophisticated	O
processing	O
.	O
</s>
<s>
Principal	O
sources	O
of	O
Gaussian	O
noise	O
in	O
digital	B-Algorithm
images	I-Algorithm
arise	O
during	O
acquisition	O
.	O
</s>
<s>
A	O
typical	O
model	O
of	O
image	B-Algorithm
noise	I-Algorithm
is	O
Gaussian	O
,	O
additive	O
,	O
independent	O
at	O
each	O
pixel	B-Algorithm
,	O
and	O
independent	O
of	O
the	O
signal	O
intensity	O
,	O
caused	O
primarily	O
by	O
Johnson	O
–	O
Nyquist	O
noise	O
(	O
thermal	O
noise	O
)	O
,	O
including	O
that	O
which	O
comes	O
from	O
the	O
reset	O
noise	O
of	O
capacitors	O
(	O
"	O
kTC	O
noise	O
"	O
)	O
.	O
</s>
<s>
Amplifier	O
noise	O
is	O
a	O
major	O
part	O
of	O
the	O
"	O
read	O
noise	O
"	O
of	O
an	O
image	B-Algorithm
sensor	I-Algorithm
,	O
that	O
is	O
,	O
of	O
the	O
constant	O
noise	O
level	O
in	O
dark	O
areas	O
of	O
the	O
image	O
.	O
</s>
<s>
At	O
higher	O
exposures	O
,	O
however	O
,	O
image	B-Algorithm
sensor	I-Algorithm
noise	O
is	O
dominated	O
by	O
shot	O
noise	O
,	O
which	O
is	O
not	O
Gaussian	O
and	O
not	O
independent	O
of	O
signal	O
intensity	O
.	O
</s>
<s>
An	O
image	O
containing	O
salt-and-pepper	O
noise	O
will	O
have	O
dark	O
pixels	B-Algorithm
in	O
bright	O
regions	O
and	O
bright	O
pixels	B-Algorithm
in	O
dark	O
regions	O
.	O
</s>
<s>
It	O
can	O
be	O
mostly	O
eliminated	O
by	O
using	O
dark	B-Algorithm
frame	I-Algorithm
subtraction	I-Algorithm
,	O
median	B-Algorithm
filtering	I-Algorithm
,	O
combined	O
median	O
and	O
mean	O
filtering	O
and	O
interpolating	O
around	O
dark/bright	O
pixels	B-Algorithm
.	O
</s>
<s>
Dead	O
pixels	B-Algorithm
in	O
an	O
LCD	B-Device
monitor	I-Device
produce	O
a	O
similar	O
,	O
but	O
non-random	O
,	O
display	O
.	O
</s>
<s>
The	O
dominant	O
noise	O
in	O
the	O
brighter	O
parts	O
of	O
an	O
image	O
from	O
an	O
image	B-Algorithm
sensor	I-Algorithm
is	O
typically	O
that	O
caused	O
by	O
statistical	O
quantum	O
fluctuations	O
,	O
that	O
is	O
,	O
variation	O
in	O
the	O
number	O
of	O
photons	B-Application
sensed	O
at	O
a	O
given	O
exposure	O
level	O
.	O
</s>
<s>
This	O
noise	O
is	O
known	O
as	O
photon	B-Application
shot	O
noise	O
.	O
</s>
<s>
Shot	O
noise	O
has	O
a	O
standard	B-General_Concept
deviation	I-General_Concept
proportional	O
to	O
the	O
square	O
root	O
of	O
the	O
image	O
intensity	O
,	O
and	O
the	O
noise	O
at	O
different	O
pixels	B-Algorithm
are	O
independent	O
of	O
one	O
another	O
.	O
</s>
<s>
In	O
addition	O
to	O
photon	B-Application
shot	O
noise	O
,	O
there	O
can	O
be	O
additional	O
shot	O
noise	O
from	O
the	O
dark	O
leakage	O
current	O
in	O
the	O
image	B-Algorithm
sensor	I-Algorithm
;	O
this	O
noise	O
is	O
sometimes	O
known	O
as	O
"	O
dark	O
shot	O
noise	O
"	O
or	O
"	O
dark-current	O
shot	O
noise	O
"	O
.	O
</s>
<s>
Dark	O
current	O
is	O
greatest	O
at	O
"	O
hot	O
pixels	B-Algorithm
"	O
within	O
the	O
image	B-Algorithm
sensor	I-Algorithm
.	O
</s>
<s>
The	O
variable	O
dark	O
charge	O
of	O
normal	O
and	O
hot	O
pixels	B-Algorithm
can	O
be	O
subtracted	O
off	O
(	O
using	O
"	O
dark	B-Algorithm
frame	I-Algorithm
subtraction	I-Algorithm
"	O
)	O
,	O
leaving	O
only	O
the	O
shot	O
noise	O
,	O
or	O
random	O
component	O
,	O
of	O
the	O
leakage	O
.	O
</s>
<s>
If	O
dark-frame	B-Algorithm
subtraction	I-Algorithm
is	O
not	O
done	O
,	O
or	O
if	O
the	O
exposure	O
time	O
is	O
long	O
enough	O
that	O
the	O
hot	O
pixel	B-Algorithm
charge	O
exceeds	O
the	O
linear	O
charge	O
capacity	O
,	O
the	O
noise	O
will	O
be	O
more	O
than	O
just	O
shot	O
noise	O
,	O
and	O
hot	O
pixels	B-Algorithm
appear	O
as	O
salt-and-pepper	O
noise	O
.	O
</s>
<s>
The	O
noise	O
caused	O
by	O
quantizing	B-Algorithm
the	O
pixels	B-Algorithm
of	O
a	O
sensed	O
image	O
to	O
a	O
number	O
of	O
discrete	O
levels	O
is	O
known	O
as	O
quantization	B-Algorithm
noise	O
.	O
</s>
<s>
If	O
film	O
grains	O
are	O
uniformly	O
distributed	O
(	O
equal	O
number	O
per	O
area	O
)	O
,	O
and	O
if	O
each	O
grain	O
has	O
an	O
equal	O
and	O
independent	O
probability	O
of	O
developing	O
to	O
a	O
dark	O
silver	O
grain	O
after	O
absorbing	O
photons	B-Application
,	O
then	O
the	O
number	O
of	O
such	O
dark	O
grains	O
in	O
an	O
area	O
will	O
be	O
random	O
with	O
a	O
binomial	O
distribution	O
.	O
</s>
<s>
For	O
example	O
,	O
image	B-Algorithm
sensors	I-Algorithm
are	O
sometimes	O
subject	O
to	O
row	O
noise	O
or	O
column	O
noise	O
.	O
</s>
<s>
long	O
exposure	O
time	O
)	O
or	O
an	O
opened	O
aperture	B-General_Concept
(	O
lower	O
f-number	O
)	O
,	O
or	O
both	O
,	O
to	O
increase	O
the	O
amount	O
of	O
light	O
(	O
photons	B-Application
)	O
captured	O
which	O
in	O
turn	O
reduces	O
the	O
impact	O
of	O
shot	O
noise	O
.	O
</s>
<s>
If	O
the	O
limits	O
of	O
shutter	O
(	O
motion	O
)	O
and	O
aperture	B-General_Concept
(	O
depth	O
of	O
field	O
)	O
have	O
been	O
reached	O
and	O
the	O
resulting	O
image	O
is	O
still	O
not	O
bright	O
enough	O
,	O
then	O
higher	O
gain	O
(	O
ISO	O
sensitivity	O
)	O
should	O
be	O
used	O
to	O
reduce	O
read	O
noise	O
.	O
</s>
<s>
At	O
the	O
cost	O
of	O
a	O
doubling	O
of	O
read	O
noise	O
variance	O
(	O
41%	O
increase	O
in	O
read	O
noise	O
standard	B-General_Concept
deviation	I-General_Concept
)	O
,	O
this	O
salt-and-pepper	O
noise	O
can	O
be	O
mostly	O
eliminated	O
by	O
dark	B-Algorithm
frame	I-Algorithm
subtraction	I-Algorithm
.	O
</s>
<s>
Banding	O
noise	O
,	O
similar	O
to	O
shadow	B-Algorithm
noise	I-Algorithm
,	O
can	O
be	O
introduced	O
through	O
brightening	O
shadows	O
or	O
through	O
color-balance	O
processing	O
.	O
</s>
<s>
In	O
digital	B-Device
camera	I-Device
photography	O
,	O
the	O
incoming	O
photons	B-Application
(	O
light	O
)	O
are	O
converted	O
to	O
a	O
voltage	O
.	O
</s>
<s>
This	O
voltage	O
then	O
passes	O
through	O
the	O
signal	B-Algorithm
processing	I-Algorithm
chain	I-Algorithm
of	O
the	O
digital	B-Device
camera	I-Device
and	O
is	O
digitized	O
by	O
an	O
analog-to-digital	O
converter	O
.	O
</s>
<s>
Any	O
voltage	O
fluctuations	O
in	O
the	O
signal	B-Algorithm
processing	I-Algorithm
chain	I-Algorithm
,	O
that	O
contribute	O
to	O
a	O
deviation	B-General_Concept
of	O
analog-to-digital	O
units	O
,	O
from	O
the	O
ideal	O
value	O
proportional	O
to	O
the	O
photon	B-Application
count	O
,	O
is	O
called	O
read	O
noise	O
.	O
</s>
<s>
It	O
is	O
important	O
to	O
note	O
that	O
the	O
f-number	O
is	O
indicative	O
of	O
light	O
density	O
in	O
the	O
focal	O
plane	O
(	O
e.g.	O
,	O
photons	B-Application
per	O
square	O
micron	O
)	O
.	O
</s>
<s>
With	O
constant	O
f-numbers	O
,	O
as	O
focal	B-Algorithm
length	I-Algorithm
increases	O
,	O
the	O
lens	O
aperture	B-General_Concept
diameter	O
increases	O
,	O
and	O
the	O
lens	O
collects	O
more	O
light	O
from	O
the	O
subject	O
.	O
</s>
<s>
As	O
the	O
focal	B-Algorithm
length	I-Algorithm
required	O
to	O
capture	O
a	O
scene	O
at	O
a	O
specific	O
angle	O
of	O
view	O
is	O
roughly	O
proportional	O
to	O
the	O
width	O
of	O
the	O
sensor	O
,	O
at	O
constant	O
f-number	O
the	O
amount	O
of	O
light	O
collected	O
is	O
roughly	O
proportional	O
to	O
the	O
area	O
of	O
the	O
sensor	O
,	O
resulting	O
to	O
a	O
better	O
signal	O
to	O
noise	O
ratio	O
for	O
larger	O
sensors	O
.	O
</s>
<s>
With	O
constant	O
aperture	B-General_Concept
diameters	O
,	O
the	O
amount	O
of	O
light	O
collected	O
is	O
independent	O
of	O
the	O
size	O
of	O
the	O
sensor	O
and	O
signal-to-noise	O
ratio	O
for	O
shot	O
noise	O
is	O
independent	O
of	O
sensor	O
size	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
images	O
bright	O
enough	O
to	O
be	O
in	O
the	O
shot	O
noise	O
limited	O
regime	O
,	O
when	O
the	O
image	O
is	O
scaled	O
to	O
the	O
same	O
size	O
on	O
screen	O
,	O
or	O
printed	O
at	O
the	O
same	O
size	O
,	O
the	O
pixel	B-Algorithm
count	O
makes	O
little	O
difference	O
to	O
perceptible	O
noise	O
levels	O
–	O
the	O
noise	O
depends	O
primarily	O
on	O
the	O
total	O
light	O
over	O
the	O
whole	O
sensor	O
area	O
,	O
not	O
how	O
this	O
area	O
is	O
divided	O
into	O
pixels	B-Algorithm
.	O
</s>
<s>
For	O
images	O
at	O
lower	O
signal	O
levels	O
(	O
higher	O
ISO	O
settings	O
)	O
,	O
where	O
read	O
noise	O
(	O
noise	O
floor	O
)	O
is	O
significant	O
,	O
more	O
pixels	B-Algorithm
within	O
a	O
given	O
sensor	O
area	O
will	O
make	O
the	O
image	O
noisier	O
if	O
the	O
per	O
pixel	B-Algorithm
read	O
noise	O
is	O
the	O
same	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
noise	O
level	O
produced	O
by	O
a	O
Four	B-Architecture
Thirds	I-Architecture
sensor	O
at	O
ISO	O
800	O
is	O
roughly	O
equivalent	O
to	O
that	O
produced	O
by	O
a	O
full	B-Algorithm
frame	I-Algorithm
sensor	O
(	O
with	O
roughly	O
four	O
times	O
the	O
area	O
)	O
at	O
ISO	O
3200	O
,	O
and	O
that	O
produced	O
by	O
a	O
1/2.5	O
"	O
compact	O
camera	B-Algorithm
sensor	I-Algorithm
(	O
with	O
roughly	O
1/16	O
the	O
area	O
)	O
at	O
ISO	O
100	O
.	O
</s>
<s>
All	O
cameras	O
will	O
have	O
roughly	O
the	O
same	O
ISO	O
setting	O
for	O
a	O
given	O
scene	O
at	O
the	O
same	O
shutter	O
speed	O
and	O
the	O
same	O
f-number	O
-	O
resulting	O
in	O
substantially	O
less	O
noise	O
with	O
the	O
full	B-Algorithm
frame	I-Algorithm
camera	O
.	O
</s>
<s>
Conversely	O
,	O
if	O
all	O
cameras	O
were	O
using	O
lenses	O
with	O
the	O
same	O
aperture	B-General_Concept
diameter	O
,	O
the	O
ISO	O
settings	O
would	O
be	O
different	O
across	O
the	O
cameras	O
,	O
but	O
the	O
noise	O
levels	O
would	O
be	O
roughly	O
equivalent	O
.	O
</s>
<s>
The	O
image	B-Algorithm
sensor	I-Algorithm
has	O
individual	O
photosites	B-Algorithm
to	O
collect	O
light	O
from	O
a	O
given	O
area	O
.	O
</s>
<s>
Temperature	O
can	O
also	O
have	O
an	O
effect	O
on	O
the	O
amount	O
of	O
noise	O
produced	O
by	O
an	O
image	B-Algorithm
sensor	I-Algorithm
due	O
to	O
leakage	O
.	O
</s>
<s>
Most	O
algorithms	O
for	O
converting	O
image	B-Algorithm
sensor	I-Algorithm
data	O
to	O
an	O
image	O
,	O
whether	O
in-camera	O
or	O
on	O
a	O
computer	O
,	O
involve	O
some	O
form	O
of	O
noise	O
reduction	O
.	O
</s>
<s>
There	O
are	O
many	O
procedures	O
for	O
this	O
,	O
but	O
all	O
attempt	O
to	O
determine	O
whether	O
the	O
actual	O
differences	O
in	O
pixel	B-Algorithm
values	O
constitute	O
noise	O
or	O
real	O
photographic	O
detail	O
,	O
and	O
average	O
out	O
the	O
former	O
while	O
attempting	O
to	O
preserve	O
the	O
latter	O
.	O
</s>
<s>
If	O
this	O
is	O
a	O
single	O
pixel	B-Algorithm
,	O
it	O
is	O
likely	O
(	O
but	O
not	O
certain	O
)	O
to	O
be	O
spurious	O
and	O
noise	O
;	O
if	O
it	O
covers	O
a	O
few	O
pixels	B-Algorithm
in	O
an	O
absolutely	O
regular	O
shape	O
,	O
it	O
may	O
be	O
a	O
defect	O
in	O
a	O
group	O
of	O
pixels	B-Algorithm
in	O
the	O
image-taking	O
sensor	O
(	O
spurious	O
and	O
unwanted	O
,	O
but	O
not	O
strictly	O
noise	O
)	O
;	O
if	O
it	O
is	O
irregular	O
,	O
it	O
may	O
be	O
more	O
likely	O
to	O
be	O
a	O
true	O
feature	O
of	O
the	O
image	O
.	O
</s>
<s>
High	O
levels	O
of	O
noise	O
are	O
almost	O
always	O
undesirable	O
,	O
but	O
there	O
are	O
cases	O
when	O
a	O
certain	O
amount	O
of	O
noise	O
is	O
useful	O
,	O
for	O
example	O
to	O
prevent	O
discretization	B-Algorithm
artifacts	B-Algorithm
(	O
color	O
banding	O
or	O
posterization	B-Algorithm
)	O
.	O
</s>
<s>
Some	O
noise	O
also	O
increases	O
acutance	B-Algorithm
(	O
apparent	O
sharpness	O
)	O
.	O
</s>
<s>
An	O
image	B-Algorithm
sensor	I-Algorithm
in	O
a	O
digital	B-Device
camera	I-Device
contains	O
a	O
fixed	O
amount	O
of	O
pixels	B-Algorithm
(	O
which	O
define	O
the	O
advertised	O
megapixels	O
of	O
the	O
camera	O
)	O
.	O
</s>
<s>
These	O
pixels	B-Algorithm
have	O
what	O
is	O
called	O
a	O
well	O
depth	O
.	O
</s>
<s>
The	O
pixel	B-Algorithm
well	O
can	O
be	O
thought	O
of	O
as	O
a	O
bucket	O
.	O
</s>
<s>
The	O
ISO	O
setting	O
on	O
a	O
digital	B-Device
camera	I-Device
is	O
the	O
first	O
(	O
and	O
sometimes	O
only	O
)	O
user	O
adjustable	O
(	O
analog	O
)	O
gain	O
setting	O
in	O
the	O
signal	B-Algorithm
processing	I-Algorithm
chain	I-Algorithm
.	O
</s>
<s>
It	O
determines	O
the	O
amount	O
of	O
gain	O
applied	O
to	O
the	O
voltage	O
output	O
from	O
the	O
image	B-Algorithm
sensor	I-Algorithm
and	O
has	O
a	O
direct	O
effect	O
on	O
read	O
noise	O
.	O
</s>
<s>
All	O
signal	O
processing	O
units	O
within	O
a	O
digital	B-Device
camera	I-Device
system	O
have	O
a	O
noise	O
floor	O
.	O
</s>
<s>
In	O
bright	O
sunny	O
conditions	O
,	O
a	O
slow	O
shutter	O
speed	O
,	O
wide	O
open	O
aperture	B-General_Concept
,	O
or	O
some	O
combination	O
of	O
all	O
three	O
,	O
there	O
can	O
be	O
sufficient	O
photons	B-Application
hitting	O
the	O
image	B-Algorithm
sensor	I-Algorithm
to	O
completely	O
fill	O
,	O
or	O
otherwise	O
reach	O
near	O
capacity	O
of	O
the	O
pixel	B-Algorithm
wells	O
.	O
</s>
<s>
If	O
the	O
capacity	O
of	O
the	O
pixel	B-Algorithm
wells	O
is	O
exceeded	O
,	O
this	O
equates	O
to	O
over	O
exposure	O
.	O
</s>
<s>
When	O
the	O
pixel	B-Algorithm
wells	O
are	O
at	O
near	O
capacity	O
,	O
the	O
photons	B-Application
themselves	O
that	O
have	O
been	O
exposed	O
to	O
the	O
image	B-Algorithm
sensor	I-Algorithm
,	O
generate	O
enough	O
energy	O
to	O
excite	O
the	O
emission	O
of	O
electrons	O
in	O
the	O
image	B-Algorithm
sensor	I-Algorithm
and	O
generate	O
sufficient	O
voltage	O
at	O
the	O
image	B-Algorithm
sensor	I-Algorithm
output	O
,	O
equating	O
to	O
a	O
lack	O
of	O
need	O
for	O
ISO	O
gain	O
(	O
higher	O
ISO	O
above	O
the	O
base	O
setting	O
of	O
the	O
camera	O
)	O
.	O
</s>
<s>
This	O
equates	O
to	O
a	O
sufficient	O
signal	O
level	O
(	O
from	O
the	O
image	B-Algorithm
sensor	I-Algorithm
)	O
which	O
is	O
passed	O
through	O
the	O
remaining	O
signal	O
processing	O
electronics	O
,	O
resulting	O
in	O
a	O
high	O
signal-to-noise	O
ratio	O
,	O
or	O
low	O
noise	O
,	O
or	O
optimal	O
exposure	O
.	O
</s>
<s>
Conversely	O
,	O
in	O
darker	O
conditions	O
,	O
faster	O
shutter	O
speeds	O
,	O
closed	O
apertures	B-General_Concept
,	O
or	O
some	O
combination	O
of	O
all	O
three	O
,	O
there	O
can	O
be	O
a	O
lack	O
of	O
sufficient	O
photons	B-Application
hitting	O
the	O
image	B-Algorithm
sensor	I-Algorithm
to	O
generate	O
a	O
suitable	O
voltage	O
from	O
the	O
image	B-Algorithm
sensor	I-Algorithm
to	O
overcome	O
the	O
noise	O
floor	O
of	O
the	O
signal	B-Algorithm
chain	I-Algorithm
,	O
resulting	O
in	O
a	O
low	O
signal-to-noise	O
ratio	O
,	O
or	O
high	O
noise	O
(	O
predominately	O
read	O
noise	O
)	O
.	O
</s>
<s>
In	O
these	O
conditions	O
,	O
increasing	O
ISO	O
gain	O
(	O
higher	O
ISO	O
setting	O
)	O
will	O
increase	O
the	O
image	O
quality	O
of	O
the	O
output	O
image	O
,	O
as	O
the	O
ISO	O
gain	O
will	O
amplify	O
the	O
low	O
voltage	O
from	O
the	O
image	B-Algorithm
sensor	I-Algorithm
and	O
generate	O
a	O
higher	O
signal-to-noise	O
ratio	O
through	O
the	O
remaining	O
signal	O
processing	O
electronics	O
.	O
</s>
