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研究生:陳昆賜
研究生(外文):Kun-Cih Chen
論文名稱:Two-stage signal restoration based on a modified median filter
論文名稱(外文):Two-stage signal restoration based on a modified median filter
指導教授:陳春樹
指導教授(外文):Chun-Shu Chen
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:數學系所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:38
中文關鍵詞:變異數罰則有效的自由度高斯混和分配廣義的Stein不偏風險估計值中位數過濾法平滑樣條
外文關鍵詞:Covariance penaltyeffective degrees of freedomGaussian mixturesgeneralized Stein’s unbiased risk estimatormedian filtersmoothing splines
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在訊號還原的過程中,如何去除訊號中隱含的雜訊並且盡可能的使還原後的訊號接
近真實的訊號是一個重要的問題,其中中位數過濾法(median filter)是一個很受歡迎的去除雜訊無母數方法,特別是在觀測到的資料中含有離群值或有厚尾分配的特性
時。除此之外,平滑樣條法(smoothing splines)也是一個去除雜訊的無母數方法。然而我們發現中位數過濾法與平滑樣條法在不同訊號類型上的表現並沒有那一個方
法永遠具有較佳的表現。因此,我們提出一個兩階段的訊號還原方法,其中平滑樣
條法被再次使用去擷取中位數過濾法估計值與平滑樣條法估計值的差距中隱含的訊
息。然後根據一個L2風險的近似不偏估計量,我們提出一個修正的中位數過濾法。
模擬實驗的結果與實際資料的分析說明了我們所提出方法的有效性與可行性。
Median filter is a popular technique for signal restoration especially when outliers and heavy-tail behaviors occur within the observed data. Moreover, the smoothing spline
method is also an alternative technique for recovering the underlying curve. Interestingly, we found that neither median filter nor smoothing splines dominates each other. Therefore, in this thesis we propose a two-stage procedure for signal denoising,in which the smoothing spline method is reused to capture residual information between median filter and smoothing splines. Then, a modified median filter is proposed to construct the underlying signals based on an approximate unbiased estimator of L2-risk. Simulated data sets are used to illustrate the superiority of the proposed
method and some comparisons are also made with other competitors. Finally, a real data example is applied for illustration.
Contents
1 Introduction 1
2 Signal Restoration Methods 4
2.1 Median Filter . . . . . . . . . . . . . . . . . . . . .4
2.1.1 Choice of the Span Parameter . . . . . . . . . . . . 6
2.1.2 Distributions of Errors . . . . . . . . . . . . . . .9
2.2 Smoothing Splines . . . . . . . . . . . . . . . . . . 11
2.2.1 Choice of the Smoothing Parameter . . . . . . . . . 12
3 A Modified Median Filter 14
3.1 Two-stage Denoising Method . . . . . . . . . . . . . .14
3.2 Computational Procedures . . . . . . . . . . . . . . .16
4 Simulation 17
4.1 Simulation Scenarios . . . . . . . . . . . . . . . . .17
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . 21
5 Real Data Analysis 33
6 Conclusion 35

List of Tables
1 The log of AMSE-values of estimates under various simulation scenarios
for recovering the blocks function, where the values in parentheses are
the corresponding standard errors. . . . . . . . . . . . . . . . . . . . . . 29
2 The log of AMSE-values of estimates under various simulation scenarios
for recovering the doppler function, where the values in parentheses are
the corresponding standard errors. . . . . . . . . . . . . . . . . . . . . . 30

List of Figures
1 The blocks function and the generated data sets under different SNR
values. (a) blocks function; (b) SNR=3; (c) SNR=7; (d) SNR=12. . . . 19
2 The doppler function and the generated data sets under different SNR
values. (a) doppler function; (b) SNR=3; (c) SNR=7; (d) SNR=12. . . 20
3 The recovering results of GSURE, SSP, and OUR for the blocks function
with SNR=3. (a) r=1; (b) r=3; (c) r=5; (d) r=7; (e) r=10. . . . . 23
4 The recovering results of GSURE, SSP, and OUR for the blocks function
with SNR=7. (a) r=1; (b) r=3; (c) r=5; (d) r=7; (e) r=10. . . . . 24
5 The recovering results of GSURE, SSP, and OUR for the blocks function
with SNR=12. (a) r=1; (b) r=3; (c) r=5; (d) r=7; (e) r=10. . . . . 25
6 The recovering results of GSURE, SSP, and OUR for the doppler function
with SNR=3. (a) r=1; (b) r=3; (c) r=5; (d) r=7; (e) r=10. . . . . 26
7 The recovering results of GSURE, SSP, and OUR for the doppler function
with SNR=7. (a) r=1; (b) r=3; (c) r=5; (d) r=7; (e) r=10. . . . . 27
8 The recovering results of GSURE, SSP, and OUR for the doppler function
with SNR=12. (a) r=1; (b) r=3; (c) r=5; (d) r=7; (e) r=10. . . . . 28
9 The scatter plots of log AMSE-values of estimates under various simulation
scenarios for recovering the blocks function. (a) SNR=3; (b)
SNR=7; (c) SNR=12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
10 The scatter plots of log AMSE-values of estimates under various simulation
scenarios for recovering the doppler function. (a) SNR=3; (b)
SNR=7; (c) SNR=12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
11 The scatter plot of the OSL dating signal data and the recovering results
of GSURE, SSP, and OUR. . . . . . . . . . . . . . . . . . . . . . 34
Birg´e, L. and Massart, P. (2007). Minimal penalties for Gaussion model selection.Probability Theory and Related Fields, 138, 33-73.
Chen, C. S. and Huang, H. C. (2011). An improved Cp criterion for spline smoothing. Journal of Statistical Planning and Inference, 141, 445-452.
Choi, J. H., Duller, G. A. T., and Wintle, A. G. (2006). Analysis of quartz LM-OSL curves. Ancient TL, 24, 9-20.
Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions:estimating the correct degree of smoothing by the method of generalized crossvalidation. Numerische Mathematik, 31, 377-403.
Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-456.
Efron, B. (2001). Selection criteria for scatterplot smoothers. Annals of Statistics, 29, 470-504.
Huang, H. C. and Lee, Thomas C. M. (2006). Data adaptive median filters for signal and image denoising using a generalized SURE criterion. IEEE Signal Processing Letters, 13, 561-564.
Jobson, J. D. (1991). Applied Multivariate Data Analysis Volume I Regression and Experimental Design. Springer-Verlag: New York.
Kou, S. C. (2003). On the efficiency of selection criteria in spline regression. Probability Theory and Related Fields, 127, 153-176.
Li, K. C. (1986). Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing. Annals of Statistics, 14,
1101-1112.
Li, S. H. and Li, B. (2006). Dose measurement using the fast component of LM-OSL signals from quartz. Radiation Measurements, 41, 534-541.
Mallows, C. (1973). Some comments on Cp. Technometrics, 15, 661-675.
Peng, J. and Han, F. Q. (2013). Selections of fast-component OSL signal using sediments from the south edge of Tengger Desert. Acta Geoscientica Sinica, 34(6), 757-762.
Reeves, S. J. (1995). On the selection of median structure for image filtering. IEEE Transactions on Circuits Systems II: Analog and Digital Signal Processing, 42, 556-558.
Shen, X. and Huang, H. C. (2006). Optimal model assessment, selection and combination. Journal of the American Statistical Association, 101, 554-568.
Silverman, B. (1981). A fast and efficient cross-validation method for smoothing parameter choice in spline regression. Journal of the American Statistical Association, 79, 584-589.
Starck, J. L., Candes, E. J., and Donoho, D. L. (2002). The curvelet transform for image denoising. IEEE Transaction on Image Processing, 11(6), 670-684.
Stein, C. M. (1981). Estimation of the mean of a multivariatenormal distribution. Annals of Statistics, 9, 1135-1151.
Tokuyasu, K., Tanaka, K., Tsukamoto, S., and Murray, A. (2010). The characteristics of OSL signal from quartz grains extracted from modern sediments in Japan. Geochronometria, 37, 13-19.
Wahba, G. (1985). A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Annals of Statistics,13, 1378-1402.
Wand, M. P. and Jones, M. C. (1995). Kernel smoothing. Chapman &; Hall, New York.
Wecker, W. and Ansley, C. (1983). The signal extraction approach to nonlinear regression and spline smoothing. Journal of the American Statistical Association,78, 81-89.
Yang, Y. and Zheng, Z. G. (1992), Asymptotic properties for cross-validated nearest neighbor median estimates in nonparametric regression: the L1-view, in Probability and Statistics (eds. Jiang, Z., Yan, S., Cheng, P. et al.), Singapore: World Scientific, 242-257.
Zheng, Z. G. and Yang, Y. (1998), Cross-validation and median criterion. Statistica Sinica, 8, 907-921.




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