1 / 23

Long-Range Prediction for Real-Time MPEG Video Traffic: An H  Filter Approach

Long-Range Prediction for Real-Time MPEG Video Traffic: An H  Filter Approach. Chih-Hu Wang ( 王志湖 ), Bor-Sen Chen ( 陳博現 ), Bore-Kuen Lee ( 李柏坤 ), Tsu-Tian Lee ( 李祖添 ), Chien-Nan Jimmy Liu ( 劉建男 ), and Chauchin Su ( 蘇朝琴 ) CSVT, Dec. 2008. Outline. Introduction Time Series

adolph
Télécharger la présentation

Long-Range Prediction for Real-Time MPEG Video Traffic: An H  Filter Approach

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Long-Range Prediction for Real-Time MPEG Video Traffic: An H Filter Approach Chih-Hu Wang (王志湖), Bor-Sen Chen (陳博現), Bore-Kuen Lee(李柏坤), Tsu-Tian Lee(李祖添), Chien-Nan Jimmy Liu (劉建男), and Chauchin Su (蘇朝琴) CSVT, Dec. 2008

  2. Outline • Introduction • Time Series • Time Series Model of MPEG Video Stream • State-Space Model • H Estimation • Neural Networks • Performance Comparisons • References

  3. Introduction • Video traffic • Example of CBR (H.264) and VBR (MPEG-1) • Goal: Predict the size n-th frame using time series

  4. Time Series • A time series is a set of observation xt, each one being recorded at a specified time t. [13] • Examples of time series model • Random walk model with zero mean • St = X1 + X2 + … + Xt, where {Xt} is iid noise. • Model with trend and seasonality • Xt = mt + Yt. (Trend component + Zero mean value) LSE Residual Seasonal model

  5. Time Series Model of MPEG Video Stream (1/4) • Video stream • Traffic prediction • y(n+td) = a(n+td) + c(n+td) + d(n+td) + w(n+td) • y(n+td): the number of bits of the (n+td)-th frame. • a(n+td): the local linear trend component. • c(n+td): the long-term periodical component. • d(n+td): the short-term periodical component. • w(n+td): the residual modeling error or noise. I B … B P B … B P B … B P … B I K N = +

  6. Time Series Model of MPEG Video Stream (2/4) • Local linear trend • a(n+td) = a(n) +b(n)td + v(n) • b(n): slop of the linear trend • b(n) can be modeled by the random walk model in practical video sequences. • b(n+1) = b(n) + u(n) • u(n) is an iid process with zero mean • c(n+td) = c(n+td-N), t=1toNc(t+n+td) = 0 • d(n+td) = d(n+td-K), t=1toKd(t+n+td) = 0

  7. Time Series Model of MPEG Video Stream (3/4) • Start from td = 1 • y(n+1) = a(n+1) + c(n+1) + d(n+1) + w(n+1) y(n) = GX(n) + w(n) a(n) b(n) c(n) c(n-1) … c(n-N+2) d(n) d(n-1) … d(n-K+2) y(n) = (1 0 1 0 … 0 1 0 … 0) + w(n) N-2 K-2 G X(n)

  8. Time Series Model of MPEG Video Stream (4/4) • X(n+1) = FX(n) + BV(n) X(n+1) F X(n) B V(n) 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 … 0 0 0 0 0 0 0 1 0 0 0 0 … 0 0 0 0 a(n+1) b(n+1) c(n+1) c(n) … c(n-N+3) d(n+1) d(n) … d(n-K+3) a(n) b(n) c(n) c(n-1) … c(n-N+2) d(n) d(n-1) … d(n-K+2) -1 … -1 -1 1 0 … 0 0 0 1 … 0 … 1 0 0 0 … 0 1 0 v(n) u(n) r(n) m(n) N-2 N-2 N-2 = + -1 … -1 -1 1 0 … 0 0 0 1 … 0 … 1 0 0 0 … 0 1 0 N-2 K-2 K-2 K-2 K-2 ps. t=1toNc(t+n+td) = 0  c(n+1+td) = -c(n+2+td) - … - c(n+N+td)

  9. State-Space Model (1/2) • State-space model • X(n+1) = FX(n) + BV(n) y(n) = GX(n) + w(n) • Goal: • Estimate • Obtain • Obtain and • Finally,

  10. State-Space Model (2/2) • State-space model [13] • Observation equation: express the observation Yt as a linear function of a state variable Xt plus noise. • Yt = GtXt + Wt, t = 1, 2, … • State equation: determine the state Xt+1 at time t+1 in terms of the Xt and noise. • Xt+1 = FtXt + Vt, t = 1, 2, …

  11. H Estimation (1/4) • Definition: H norm of a transform operator T[12] • ||T|| = sup ||T(x)||/||x|| • The maximum energy gain from the input x to the output T(x) T x T(x)

  12. H Estimation (2/4) • State-space model • y(n) = GX(n) + w(n) • X(n+1) = FX(n) + BV(n) • Transfer matrix from disturbances to filtered errors [12] • Optimal H problem [12] • Find optimal that minimize ||T|| T

  13. H Estimation (3/4) • Sub-optimal H problem [12] • Find sub-optimal that achieves ||T||< r

  14. H Estimation (4/4) • Solution of the sub-optimal H problem • P(n) needs to satisfy • 2 is a free designed parameter

  15. Neural Networks (1/4) • Neuron model [15] p1 w1,1 w1,2 n a p2  f … b w1,R pR a = f(Wp+b) 1 a a a 1 1 1 n n n -1 -1 -1 linear transfer function tangent sigmoid transfer function log sigmoid transfer function

  16. Neural Networks (2/4) • Focused time-delay neural network (FTDNN) • # of parameters: 312 weights and 48 bias constants N1 b D1 N2 b D2 N25 … … … b D12 w’1,1w’1,2 … w’1,24 w1,1w1,2 … w1,12 w2,1w2,2 … w2.12 … w24,1w24.2 … w24.12 N24 Tapped delay line b

  17. Neural Networks (3/4) • Nonlinear autoregressive network with exogenous inputs (NARX) • # of parameters: 600 weights and 48 bias constants TDL N1 b … N2 12 b N25 TDL … w1,1 … w1,24 … w24,1 … w24,24 w’1,1w’1,2 … w’1,24 b … N24 12 b

  18. Neural Networks (4/4) • Elman network • # of parameters: 888 weights and 48 bias constants D N1 b … 24 N2 b N25 … b w1,1 … w1,36 … w24,1 … w24,36 … 12 N24 b

  19. Performance Comparisons (1/4) • Time comparison

  20. Performance Comparisons (2/4) • MPEG-1 dino star ‘x’ FTDNN ‘*’ Elman ‘+’ NARX ‘o’ H mr.bean soccer atp race

  21. Performance Comparisons (3/4)

  22. Performance Comparisons (4/4) • MPEG-4 aladdin dusk contact Jurassic soccer star4

  23. References • [13] P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting. New York: Springer, 1996. • [12] B. Hassibi, A. H. Sayed, and T. Kailath, “Linear estimation in Krein spaces-Part II: Application,” IEEE Trans. Automat. Contr., 1996. • [15] H. Demuth, M. Beale, and M. Hagan, Neural Network Toolbox 5: User’s Guide. Natick, MA: The MathWorks, 2007.

More Related