Information Technology Reference
In-Depth Information
2
Optimal Multi-scale Decomposition of Real Time Video
Traffic
Multi-scale decomposition of signal comes from the wavelet theory [9], and wavelet
packet decomposition is based on wavelet decomposition. Combined with a rigorous
mathematical theory and numerical calculations, wavelet packet decomposition can
be used to conduct multi-level signal decomposition in different frequency bands.
2.1
Analysis of Video Traffic Wavelet Packet Decomposition
Prediction commonly use linear time series analysis and nonlinear time series analysis
method. The former assumes that the sequence is a linear correlation structure, the
latter assumes that the series has chaos characteristic. For signals with long-range
dependence, wavelet decomposition is an important method to change its long-range
dependence. In this paper, we adopt α/ʲ traffic model to describe the video traffic
[10]
.
Alpha components of traffic is highly non-Gaussian and entirely responsible for the
bursty behavior, ʲ component is a aggregation of low-rate traffics, and has a long-
range dependence, its marginal distribution can be well approximated with a Gaussian
distribution, so ʲ traffic can be expressed using a fractal Gaussian approximation. An
aggregate traffic can be decomposed into[10]:
Total
=
α
+
β
(1)
traffic
traffic
traffic
Literature [11] mentioned that for a video traffic expressed with α/ʲ traffic model, if
ʲ traffic obey fractal Gaussian distribution and α traffic obey the Gaussian distribu-
tion, wavelet transform coefficients is short-range dependence in the same scale after
wavelet transform. Thus, if we predict wavelet transform coefficients with short-range
dependence using traditional series prediction method, we will be able to predict both
the variation trend of video traffic and the bursty behavior of video traffic.
2.2
Optimal Wavelet Packet Decomposition of Video Traffic
The quality of signal decomposition and time-frequency analysis is heavily dependent
on the choice of the fundamental function, so it is necessary to solve two problems,
one is how to evaluate the pros and cons of a basis, the second is how to find the
optimal basis in a wavelet library quickly. According to the selection principle of
optimal basis [12], the cost function of video signals is defined as the Shannon entro-
py of wavelet packet coefficient sequence
uu
=
{}
j
, which is generated by decomposi-
tion of video signal
xt
using an orthogonal wavelet basis.
()
2
2
PP
log
=
0
Definition 1:
set sequence
uu
=
{
}
,
Pu u
=
/
, if
P
=
0
,
, shannon
j
j
j
j
j
entropy of
u
is defined as:
