Spatio-temporal joint filter for noise reduction
A spatio-temporal joint filter and a spatial joint filter for noise reduction are disclosed. The spatio-temporal joint filter includes a spatial joint filter including the first and second sub filters having different characteristics and includes a temporal joint filter. When the present invention is adequately used, an edge/detail region of an image is well preserved, an aggressive noise reduction is performed on a flat region, and the temporal flicker problems are eliminated. Additionally, it has an intrinsic motion compensation effect by using the spatio-temporal correlation between the adjacent frames.
1. A spatio-temporal joint filter for noise reduction comprising: a spatial joint filter including
a first filter connected to an input determining a first weighted average of current support region signals of said input using first weighting factors, said current support region signals being included in a current frame, and
a second filter connected to said input and an output of said first filter determining a second weighted sum of said input signal and said first weighted average using a second weighting factor that depends on an original signal variance and a noise variance; a temporal joint filter including
a third filter connected to an output of said second filter determining a third weighted average of said second weighted sum and previous support region signals of said input signal using third weighting factors, said previous support region signals being included in a previous frame, and
a fourth filter connected to an output of said second filter determining a fourth weighted sum of said second weighted sum and said third weighted average using a fourth weighting factor that depends on a spatio-temporal signal variance and said noise variance wherein said fourth weighted sum f o (i,j,t) is determined using the following equation:
α
(
i
,
j
,
t
)
=
σ
f
2
(
i
,
j
,
t
)
σ
f
2
(
i
,
j
,
t
)
+
σ
n
2
where
f s (i,j,t) is said second weighted sum,
μ T (i,j,t) is said third weighted average,
σ 2 ST (i,j,t) is said spatio-temporal signal variance, and
σ 2 n is a noise variance;
σ
ST
2
(
i
,
j
,
t
)
=
max
[
σ
f
2
(
i
,
j
,
t
)
,
σ
d
2
(
i
,
j
,
t
)
-
σ
n
2
2
]
σ
d
2
(
i
,
j
,
t
)
=
1
S
{
∑
(
i
,
j
)
∈
S
(
g
(
i
,
j
,
t
)
-
f
o
(
i
,
j
,
t
-
1
)
)
2
}
_
where
σ 2 f (i,j,t) is a original signal variance, and
f o (l,m,t−1) is a previous fourth weighted sum included in said support region of said previous frame; and
a frame memory storing said fourth weighted sum and feedbacking said fourth weighted sum to said third filter for a next frame.
2. The spatio-temporal joint filter of claim 1 , wherein said first weighted average g 1 (i,j,t) is determined using the following equation:
g1
(
i
,
j
,
t
)
=
1
W
∑
(
l
,
m
,
t
)
∈
S
ϖ
(
l
,
m
,
t
)
g
(
l
,
m
,
t
)
W
=
∑
(
l
,
m
,
t
)
∈
S
ϖ
(
l
,
m
,
t
)
where
{overscore (ω)}(l,m,t) is each first weighting factor,
g(l,m,t) is each current support region signal, and
S represents a support region of an image.
3. The spatio-temporal joint filter of claim 2 , wherein said first filter is AWA filter, and each first weighting factor {overscore (ω)}(l,m,t) is determined using the following equation:
ϖ
(
l
,
m
,
t
)
=
1
1
+
α
{
max
[
ɛ
,
(
g
(
l
,
m
,
t
)
-
g
(
i
,
j
,
t
)
)
2
]
}
where α=1 and ε=2σ n 2 , and g(i,j,t) is said input signal.
4. The spatio-temporal joint filter of claim 2 , wherein said first filter is A-MEAN filter, and each said first weighting factor {overscore (ω)}(l,m,t) is determined using the following question:
ϖ
(
l
,
m
,
t
)
=
{
1
for
x
≤
c
0
for
x
>
c
x
=
g
(
l
,
m
,
t
)
-
g
(
i
,
j
,
t
)
Where c represents a predetermined limiting factor, and g(i,j,t) is said input signal.
5. The spatio-temporal joint filter of claim 1 , wherein said second weighted sum f s (i,j,t) is determined using the following equation:
α
(
i
,
j
,
t
)
=
σ
f
2
(
i
,
j
,
t
)
σ
f
2
(
i
,
j
,
t
)
+
σ
n
2
where
g(i,j,t) is said input signal,
g 1 (i,j,t) is said first weighted average,
α(i,j,t) is said second weighting factor,
σ f 2 (i,j,t) is said original signal variance, and
σ n 2 is said noise variance.
6. The spatio-temporal joint filter of claim 5 , wherein said original signal variance σ f 2 (i,j,t) is determined using the following equation:
σ f 2 ( i,j,t )=max[σ g 2 ( i,j,t )−σ n 2 ,0]
where σ g 2 (i,j,t) is a local variance of said input signal g(i,j,t).
7. The spatio-temporal joint filter of claim 6 , wherein said local variance σ g 2 (i,j,t) is determined using the following equation:
σ
g
2
(
i
,
j
,
t
)
≅
1
S
∑
(
i
,
j
)
∈
S
g
2
(
i
,
j
,
t
)
-
[
1
S
∑
(
i
,
j
,
)
∈
S
g
(
i
,
j
,
t
)
]
2
where S represents a support region of an image of said input signal g(i,j,t).
8. The spatio-temporal joint filter of claim 1 , wherein said third weighted average μ T (i,j,t) is determined using the following equation:
μ
T
(
i
,
j
,
t
)
=
1
W
{
ϖ
o
f
s
(
i
,
j
,
t
)
+
∑
l
,
m
,
t
∈
S
ϖ
(
l
,
m
,
t
-
1
)
f
o
(
l
,
m
,
t
-
1
)
}
W
=
ϖ
o
+
∑
l
,
m
,
t
∈
S
ϖ
(
l
,
m
,
t
-
1
)
where
S represents a support region of an image,
f s (i,j,t) is said second weighted sum,
{overscore (ω)}(l,m,t−1) is each third weighting factor, and
f o (l,m,t−1) is a previous forth weighted sum included in said support region of said previous frame.
9. The spatio-temporal joint filter of claim 8 , wherein said third filter is an AWA filter, and
ϖ
o
=
1
1
+
αɛ
ϖ
(
l
,
m
,
t
-
1
)
=
1
1
+
α
{
max
[
ɛ
,
(
f
o
(
l
,
m
,
t
-
1
)
-
f
s
(
l
,
m
,
t
)
)
2
]
}
where α=1 and ε=2σ n 2 .
10. The spatio-temporal joint filter of claim 8 , wherein said third filter is an A-MEAN filter, and
ϖ
o
=
1
,
ϖ
(
l
,
m
,
t
-
1
)
=
{
1
for
x
≤
c
0
for
x
>
c
x
=
f
o
(
l
,
m
,
t
-
1
)
-
f
s
(
i
,
j
,
t
)
Where c represents a predetermined limiting factor.
11. The spatio-temporal joint filter of claim 1 , further comprising a statistic calculator providing variance signals to said first filter, second filter, third filter, and fourth filter.