Digital Signal Processing Reference
In-Depth Information
then the residuals are obtained by subtracting the central (averaged) reconstruction
in stage 1 from the original wavelet coefficients. The wavelet residuals are split
by subsampling and coded with QTCQ to produce part 2 information for each
description.
Note that the MMDSQ [
6
] also uses a similar two-stage structure. When
both descriptions are received, the second stage decoded information (part 2) is
added to the average of the description 1 (part 1) and description two (part 1) to
further enhance the reconstruction quality, which is similar to the MMDSQ central
decoding [
6
]. However, the side decoding of the proposed scheme is much different
from that of MMDSQ. In the side decoding of the proposed scheme, when only
one description is received, the reconstructed information from part 2 will also
be exploited to be added to the part 1 of the received description, which will be
shown to help reduce the side distortion in the following. In the MMDSQ [
6
],
however, when only one description is received, the second part information is
completely useless, which cannot be used for improving the side decoding and
therefore discarded.
4.3.3.2
Side Distortion Analysis
The residual errors between the original wavelet coefficients and the averaged
reconstructions from part 1 information can be represented as
e
0
D
x
x
0
D
0:5.e
1
C
e
2
/:
(4.10)
The errors are split with subsampling and then coded by QTCQ to form the
second part for each description. For simplicity, we assume the odd/even coefficient
subsampling way. For the balanced descriptions, only description 1 is considered,
while the other can be analyzed similarly. In the decoding end, the odd samples
of the second part are added to the first part of description 1. Then, description 1
becomes
x
C
e
1
C
e
0
;
foroddcoeficients
x
1
D
;
(4.11)
x
C
e
1
;
forevencoeficients
where
e
0
denotes the reconstructed counterpart of e
0
. We make the asymptotic anal-
ysis of adding the decoded odd part of central residuals to the side reconstruction,
that is,
e
0
approximates e
0
. Substituting e
0
with that in (
4.10
), we can obtain the side
distortion for description 1 as
d
1
0
D
E
h
.x
x
1
/
2
i
D
0:5E
h
.e
1
/
2
i
C
0:5E
h
.e
1
C
e
0
/
2
i
D
0:5ı
2
C
0:25ı
2
.1
/
ı
2
:
(4.12)
