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where
f
nB
,
f
n
(
B,E
1)
are the reconstructed pixel values at the encoder using only
the base layer, and the base along with the FGS layer of frame
n
, respectively.
P
nE
1
is the probability of losing the FGS layer of frame
n
.
For all the frames except the key pictures of a GOP, let us denote
f
nB u
n
v
n
as the
i
th
pixel value of the base layer of frame
n
reconstructed at the encoder.
Frames
u
n
(
<n
)and
v
n
(
>n
) are the reference pictures used in the hierarchical
prediction structure for the reconstruction of frame
n
. We will refer to these
frames (
u
n
and
v
n
) as the “true” reference pictures for frame
n
. In the decoding
process of SVC, the frames of each GOP are decoded in the order starting from
the lowest to the highest temporal level. At the decoder, if either or both of the
true reference frames are not received correctly, the non-key picture(s) will be
considered erased and will be concealed.
For the Temporal-SNR SDDE method, the
s
th
moment of the
i
th
pixel of
frame
n
when at least the base layer is received correctly is defined as
E
f
n
(
u
n
,v
n
)
s
=(1
P
v
n
)
P
nE
1
f
nB u
n
v
n
s
−
P
u
n
)(1
−
P
nE
1
)
f
n
(
B,E
1)
u
n
v
n
s
(8)
−
P
u
n
)(1
−
P
v
n
)(1
−
+(1
where,
P
u
n
and
P
v
n
are the probabilities of losing the base layer of the reference
frames
u
n
and
v
n
, respectively. Now to get the distortion per-pixel after error
concealment, we define a set
Q
=
,where
f
n
is the
frame to be concealed,
f
q
1
is the first frame,
f
q
2
isthesecondframetobeused
for concealment of
f
n
, and so on till one of the GOP ends is reached. The
s
th
moment of the
i
th
pixel using the set
Q
is defined as
E
f
n
s
=(1
{
f
n
,f
q
1
,f
q
2
,f
q
3
, ..., f
GOP end
}
P
n
)E
f
n
(
u
n
,v
n
)
s
−
P
q
1
)E
f
q
1
(
u
q
1
,v
q
1
)
s
+
1
P
n
(1
−
−
P
q
2
)E
f
q
2
(
u
q
2
,v
q
2
)
s
+
1
P
n
P
q
1
(1
(9)
−
−
+
...
+
1
E
f
i
GOP end
s
P
n
|
Q
|−
2
z
=1
P
qz
−
where
P
n
=(1
P
v
n
) is the probability of correctly receiving
the base layers of frame
n
and the base layers of its reference pictures.
−
P
n
)(1
−
P
u
n
)(1
−
5.2 SNR-Temporal SDDE
Similar to the Temporal-SNR SDDE case, in this method the base layer of all
the key pictures are assumed to be received error-free and the
s
th
moment of
the
i
th
pixel of the key pictures
n
is again calculated using Eq. (7). For all the
frames except the key pictures of a GOP, let us denote
f
nB u
(
B,E
1)
n
v
(
B,E
1)
n
as
the
i
th
pixel value of the base layer of frame
n
reconstructed at the encoder.
Frames
u
(
B,E
1)
n
(
<n
)and
v
(
B,E
1)
n
(
>n
) are the reference pictures (including
both base and FGS layers) used in the hierarchical prediction structure for the
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