跳到主要內容

臺灣博碩士論文加值系統

(3.236.225.157) 您好!臺灣時間:2022/08/15 23:55
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:張炎清
研究生(外文):Yen-Ching Chang
論文名稱:離散時間分數維度布朗運動之研究
論文名稱(外文):Studies on Discrete-Time Fractional Brownian Motion
指導教授:張翔張翔引用關係
指導教授(外文):Shyang Chang
學位類別:博士
校院名稱:國立清華大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:90
語文別:英文
論文頁數:91
中文關鍵詞:分數維度布朗運動離散時間分數維度布朗運動離散時間分數維度高斯雜訊奇異性正規性離散分數維度差分高斯雜訊
外文關鍵詞:fractional Brownian motiondiscrete-time fractional Brownian motiondiscrete-time fractional Gaussian noisesingularityregularitydiscrete fractionally differenced Gaussian noiseentropy
相關次數:
  • 被引用被引用:0
  • 點閱點閱:211
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
近年來,分數維度布朗運動(Fractional Brownian Motion,簡稱FBM)模式已經被使用在許多不同的領域。在此模式的應用上,必須估測赫斯特參數(Hurst parameter, H),此參數與碎型維度(fractal dimension, D)的關係為 。然而,由於離散時間分數維度布朗運動(discrete-time FBM,簡稱DFBM)的非穩固性(nonstationarity),因此,它的被稱為離散時間分數維度高斯雜訊(discrete-time fractional Gaussian noise,簡稱DFGN)的增量(increment)程序被引用為一個估測H的輔助工具。在此論文中,離散時間分數維度高斯雜訊與離散分數維度差分高斯雜訊(discrete fractionally differenced Gaussian noise,簡稱fdGn)的關係被分析。赫斯特參數與熵(entropy)的關係被獲得。並且證明離散時間分數維度高斯雜訊是正規的(regular)。基於此正規性,一個快速且精確的估測赫斯特參數的方法被提出。此方法擁有比最大相似估測器(maximum likelihood estimator,簡稱MLE)和移動平均(moving average,簡稱MA)法更小的計算量。此外,此方法在振幅平移是強健的(robust),且不隨時間平移而變化,並且不受功率密度函數(power spectral density,簡稱PSD)的尺度因數的影響。最後,此方法和嵌有赫斯特參數的熵數估測將被應用於外尿道括約肌(external urethral sphincter,簡稱EUS)的肌電圖(electromyogram,簡稱EMG)。這些信號來自於未受傷的成鼠和遭受脊髓損傷(spinal cord injury,簡稱SCI)的成鼠。分析顯示我們可以由此新訊息分辨未受傷與脊髓損傷的成鼠。
In recent years, fractional Brownian motion (FBM) model has been used in a large number of different disciplines. In the application of this model, it is imperative to estimate the Hurst parameter , which is directly related to fractal dimension . However, due to the nonstationarity of the discrete-time fractional Brownian motion (DFBM), its increment process, referred to as discrete-time fractional Gaussian noise (DFGN), is invoked as an auxiliary tool to estimate . In this dissertation, the relation between DFGN and discrete fractionally differenced Gaussian noise (fdGn) is analyzed. The relation between Hurst parameter and entropy is also derived. It is shown that the DFGN is regular. Based on the regularity, a fast and accurate method to estimate the parameter is proposed. This method possesses lower computational cost than maximum likelihood estimator (MLE) and moving average (MA) method. Furthermore, this method is robust under amplitude shift, invariant to time shift, and unaffected by a scaling factor in power spectral density (PSD). Finally, this method and the estimation of entropy embedded with Hurst parameter will be applied to the electromyogram (EMG) of external urethral sphincter (EUS). These signals come from intact rats and the injured ones from spinal cord injury (SCI). Analysis indicates that we can discriminate between intact and SCI rats from this new information.
Abstract i
Acknowledgements ii
List of Figures v
List of Tables ix
List of Algorithms xi
Chapter 1 Introduction 1
1.1 Fractal dimension and history.………………………......….1
1.2 Motivations………………...…………….…………………......5
1.3 Contributions of the dissertation………………………......5
1.4 Organization of the dissertation.…………………………....6
Chapter 2 Preliminaries 8
2.1 FBM and its variants.……………………………..……………..8
2.2 Levinson’s algorithm.……………………………………………10
2.3 Definitions and properties of fdGn.………………………...11
2.4 Singularity, regularity, and Wold’s decomposition………12
Chapter 3 Properties of DFGN 19
3.1 The relation between DFGN and fdGn…………………………..19
3.2 The relation between Hurst parameter and entropy………..21
3.3 The regularity of DFGN………………………………………....23
Chapter 4 Estimation of Hurst Parameter 30
4.1 Establishing a standard monotonic curve…………………...30
4.2 The performance of estimation of Hurst parameter………..33
4.3 Order selection of curve and AR model……………………….52
4.4 Applications to biomedical signal…………………………….77
Chapter 5 Conclusions and Directions for Future Research 85
Bibliography 87
Box, G. E. P. and Jenkins, G. M. 1970, Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco, 1970.
Chang, Y. C., and Chang, S. “A fast estimation algorithm on the Hurst parameter of discrete-time fractional Brownian motion,” IEEE Trans. Signal Processing, (accepted, 2001)
Chang, Y. C., and Chang, S. “The entropy of discrete-time fractional Gaussian noise and its application to the electromyogram of external urethral sphincter signals,” Journal of Biomedical Engineering- Appl., Basis, and Comm. (accepted, 2001)
Chang, S., Mao, S. T., Kuo, T. P., Hu, S. J., and Cheng, C. L. 2000, “Studies of detrusor-sphincter synergia and dyssynergia during micturition in rats via fractional Brownian motion,” IEEE Trans. Biomed. Eng. vol. 47, no. 8, pp. 1066-1073, 2000.
Chen, C. C., Daponte, J. S. and Fox, M. D. 1989, “Fractal feature analysis and classification in medical imaging,” IEEE Trans. Med. Imaging, vol. 8, no. 2, pp. 133-142, June 1989.
Chen, S. S., Keller, J. M., and Crownover, R. M. 1993, “On the calculation of fractal features from images,” IEEE Trans. Pattern Anal. Machine Intell., vol. 15, no. 10, pp. 1087-1090, Oct. 1993.
Cherbit, G., Kahane, J. -P., and Jellett, F. 1991, Fractals: Non-integral dimensions and applications. New York: John Wiley & Sons, 1991.
Cover, T. M. and Thomas, J. A. 1991, Elements of Information Theory. New York: John Wiley & Sons, 1991.
Crilly, A. J., Earnshaw, R. A., and Jones, H. 1991, Fractals and Chaos. New York: Springer-Verlag, 1991.
Deriche, M. and Tewfik, A. H. 1993, “Signal modeling with filtered discrete fractional noise processes,” IEEE Trans. Signal Processing, vol. 41, no. 9, pp.2839-2849, Sep. 1993.
Dijkerman, R. W. and Mazumdar, R. R. 1994, “On the correlation structure of the wavelet coefficients of fractional Brownian motion,” IEEE Trans. Inform. Theory, vol. 40, no. 5, pp. 1609-1612, Sep. 1994.
Doob, J. L. 1953, Stochastic Processes. New York: John Wiley & Sons, 1953.
Falconer, K. 1990, Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons, 1990.
Flandrin, P. 1989, “On the spectrum of fractional Brownian motions,” IEEE Trans. Inform. Theory, vol. 35, no. 1, pp. 197-199, Jan. 1989.
Flandrin, P. 1992, “Wavelet analysis and synthesis of fractional Brownian motion,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 910-917, Mar. 1992.
Fournier, A., Fussell, D., and Carpenter, L. 1982, “Computer rendering of stochastic models,” Graphics and Image Processing, vol. 25, n0. 6, pp. 371-384, June1982.
Gardner, W. A. 1990, Introduction to Random Processes: With Application to Signals & Systems, 2nd ed. New York: McGraw-Hill, 1990.
Gradshteyn, I. S., Ryzhik, I. M., and Jeffrey, 1994, A. Table of Integrals, Series, and Products, 5th ed. New York: Academic Press, 1994.
Granger, C. W. J. and Joyeux, R. 1980, “An introduction to long-memory time series models and fractional differencing,” J. Time Series Anal., vol. 1, no. 1, pp. 15-29, 1980.
Hosking, J. R. M. 1981, “Fractional differencing,” Biometrika, vol. 68, no. 1, pp. 165-176, 1981.
Jin, X. C., Ong, S. H., and Jayasooriah, 1995, “A practical method for estimating fractal dimension,” Patter Recognition Letters, vol. 16, pp. 457-464, 1995.
Kaplan, L. M. and Kuo, C. -C. J. 1993, “Fractal estimation from noisy data via discrete fractional Gaussian noise (DFGN) and the Harr basis,” IEEE Trans. Signal Processing, vol. 41, no. 12, pp. 3554-3562, Dec. 1993.
Kashyap, R. L. and Eom, K. B. 1989, “Texture boundary detection based on the long correlation model,” IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 1, pp. 58-67, Jan. 1989.
Kay, S. M. 1988, Modern Spectral Estimation: Theory & Application. Englewood Cliffs, New Jersey: Prentice-Hall, 1988.
Keller, J. M., Chen, S., and Crownover, R. M. 1989, “Texture description and segmentation through fractal geometry,” Comput. Graphics Image Processing, vol. 45, pp. 150-166, 1989.
Keller, J. M., Crownover, R. M., and Chen, R. Y. 1987, “Characteristics of natural scenes related to the fractal dimension,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 5, pp. 621-627, Sep. 1987.
Leu, J. S. and Papamarcou, A. 1995, “On estimating the spectral exponent of fractional Brownian motion,” IEEE Trans. Inform. Theory, vol. 41, no. 1, pp. 233-244, Jan. 1995.
Liu, S. C. and Chang, S. 1997, “Dimension estimation of discrete-time fractional Brownian motion with applications to image texture classification,” IEEE Trans. Image Processing, vol. 6, no. 8, pp. 1176-1184, Aug. 1997.
Lundahl, T., Ohley, W. J., Kay, S. M., and Siffert, R. “Fractional Brownian motion: A maximum likelihood estimator and its application to image texture,” IEEE Trans. Med. Imag.,, vol. MI-5, no. 3, pp. 152-161, Sep. 1986.
Mandelbrot, B. B. and Van Ness, J. W. 1968, “Fractional Brownian motions, fractional noises and applications,” SIAM Rev., vol. 10, pp. 422-437, Oct. 1968.
Martin, W. and Flandrin, P. 1985, “Wigner-Ville spectral analysis of nonstationary processes,” IEEE Trans. Acoust. Speech, Signal Processing, vol. ASSP-33, no. 6, pp. 1461-1470, Dec. 1985.
Masry, E. 1993, “The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion,” IEEE Trans. Inform. Theory, vol. 39, no. 1, pp.260-264, Jan. 1993.
Mathai, A. M. 1993, A Handbook of Generalized Special Functions for Statistical and Physical Sciences. New York: Oxford University Press, 1993.
Miller, K. S. and Ross, B. 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations. New York: John Wiley & Sons, 1993.
Ohanian, P. P. and Dubes, R. C. 1992, “Performance evaluation for four classes of textural features,” Pattern Recognition Society, vol. 25, no. 8, pp. 819-833, 1992.
Pentland, A. P. 1984, “Fractal-based description of natural scenes,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 6, pp. 661-674, Nov. 1984.
Priestley, M. B. 1981, Spectral Analysis and Time Series, Volume 1: Univariate Series. New York: Academic Press, 1981.
Priestley, M. B. 1981, Spectral Analysis and Time Series, Volume 2: Multivariate Series, Prediction and Control. New York: Academic Press, 1981.
Rényi, A. 1970, Probability Theory. London: North-Holland, 1970.
Samorodnitsky, G., and Taqqu, M. S. 1994, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. New York: Chapman & Hall, 1994.
Sarkar, N. and Chaudhuri, B. B. 1992, “An efficient approach to estimation fractal dimension of textural images,” Pattern Recognition Society, vol. 25, no. 9, pp. 1035-1041, 1992.
Sarkar, N. and Chaudhuri, B. B. 1994, “ An efficient differential box-counting approach to compute fractal dimension of image,” IEEE Trans. System, Man, and Cybernetics, vol. 24, no. 1, pp. 115-120, Jan. 1994.
Shiryaev, A. N. 1996, Probability, 2nd ed., translated by R. P. Boas. New York: Springer-Verlag, 1996.
Tewfik, A. H. and Kim, M. 1992, “Correlation structure of the discrete wavelet coefficients of fractional Brownian motion,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 904-909, Mar. 1992.
Therrien, C. W. 1992, Discrete Random Signals and Statistical Signal Processing. Englewood Cliffs, New Jersey: Prentice-Hall, 1992.
Wornell, G. W. and Oppenheim, A. V. 1992, “Estimation of fractal signals from noisy measurements using wavelets,” IEEE Trans. Signal Processing, vol. 40, no. 3, pp. 611-623, Mar. 1992.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top