<s>
In	O
signal	O
processing	O
,	O
particularly	O
image	B-Algorithm
processing	I-Algorithm
,	O
total	B-Algorithm
variation	I-Algorithm
denoising	I-Algorithm
,	O
also	O
known	O
as	O
total	B-Algorithm
variation	I-Algorithm
regularization	I-Algorithm
or	O
total	B-Algorithm
variation	I-Algorithm
filtering	I-Algorithm
,	O
is	O
a	O
noise	O
removal	O
process	O
(	O
filter	O
)	O
.	O
</s>
<s>
It	O
is	O
based	O
on	O
the	O
principle	O
that	O
signals	O
with	O
excessive	O
and	O
possibly	O
spurious	O
detail	O
have	O
high	O
total	O
variation	O
,	O
that	O
is	O
,	O
the	O
integral	O
of	O
the	O
absolute	O
image	B-Algorithm
gradient	I-Algorithm
is	O
high	O
.	O
</s>
<s>
According	O
to	O
this	O
principle	O
,	O
reducing	O
the	O
total	O
variation	O
of	O
the	O
signal	O
—	O
subject	O
to	O
it	O
being	O
a	O
close	O
match	O
to	O
the	O
original	O
signal	O
—	O
removes	O
unwanted	O
detail	O
whilst	O
preserving	O
important	O
details	O
such	O
as	O
edges	B-Algorithm
.	O
</s>
<s>
This	O
noise	O
removal	O
technique	O
has	O
advantages	O
over	O
simple	O
techniques	O
such	O
as	O
linear	B-Error_Name
smoothing	I-Error_Name
or	O
median	B-Algorithm
filtering	I-Algorithm
which	O
reduce	O
noise	O
but	O
at	O
the	O
same	O
time	O
smooth	O
away	O
edges	B-Algorithm
to	O
a	O
greater	O
or	O
lesser	O
degree	O
.	O
</s>
<s>
By	O
contrast	O
,	O
total	B-Algorithm
variation	I-Algorithm
denoising	I-Algorithm
is	O
a	O
remarkably	O
effective	O
edge-preserving	B-Algorithm
filter	I-Algorithm
,	O
i.e.	O
,	O
simultaneously	O
preserving	O
edges	B-Algorithm
whilst	O
smoothing	O
away	O
noise	O
in	O
flat	O
regions	O
,	O
even	O
at	O
low	O
signal-to-noise	O
ratios	O
.	O
</s>
<s>
Given	O
an	O
input	O
signal	O
,	O
the	O
goal	O
of	O
total	B-Algorithm
variation	I-Algorithm
denoising	I-Algorithm
is	O
to	O
find	O
an	O
approximation	O
,	O
call	O
it	O
,	O
that	O
has	O
smaller	O
total	O
variation	O
than	O
but	O
is	O
"	O
close	O
"	O
to	O
.	O
</s>
<s>
A	O
recent	O
algorithm	O
that	O
solves	O
this	O
is	O
known	O
as	O
the	O
primal	B-Algorithm
dual	I-Algorithm
method	I-Algorithm
.	O
</s>
