Information Technology Reference
In-Depth Information
Using this inequality, equation (14) can be approximated as follows:
s
(1
κ
1
2
σ
−
ρ
)
β
1
(
m
)
m
Since
m
is the ratio of downsampled frame-rate
F
to maximum frame-rate
F
0
,we
have
s
(1
−
ρ
κ
1
2
σ
)
β
1
(
m
)
F
F
0
In a similar way, we have
2
σ
s
(1
−
ρ
)
β
2
(
m
)
2
κ
2
γφ
(
x
)
F
F
0
where
1.
Next, let us consider
γ
is 1 or
−
3
(
m
). Since we assume that the noise element
n
(
m
) is
statistically independent of the video signal, the averaging procedure denoted by
equation (11) reduces
n
(
m
) as follows:
β
X
/
L
i
=1
∑
n
0
m
n
(
m
)
2
=
x
∈
B
[
i
]
=
X
n
0
F
0
F
where,
n
0
is the noise signal included in the sequence at frame-rate
F
0
.
We have the following approximation of prediction error per pixel:
X
/
L
i
=1
σ
1
X
m
[
i
]=
ˆ
1
F
−
1
+
ˆ
2
F
−
1
/
2
+
ˆ
3
F
+
ˆ
β
β
β
β
(14)
4
ˆ
ˆ
β
3
,and
ˆ
ˆ
where,
β
1
,
β
2
,
β
4
are as follows:
s
(1
2
κ
1
σ
−
ρ
)
ˆ
β
1
=
XF
0
2
s
(1
2
κ
2
γφ
(
x
)
σ
−
ρ
)
ˆ
β
2
=
X
F
0
n
0
F
0
ˆ
β
3
=
X
/
L
i
=1
∑
1
X
ˆ
2
B
[
i
]
{
φ
}
β
4
=
(
x
)
x
∈
Let us consider the effect of noise components in our models: the third term of
equation (10) and the third term of equation (14). The former is constant i.e.
