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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 貝蘇章(Soo-Chang Pei) | |
| dc.contributor.author | Shih-Lung Hsu | en |
| dc.contributor.author | 許仕龍 | zh_TW |
| dc.date.accessioned | 2021-06-16T23:44:08Z | - |
| dc.date.available | 2013-08-01 | |
| dc.date.copyright | 2012-08-01 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-24 | |
| dc.identifier.citation | [1] Mama Foupouagnigni, “On Difference and Differential Equations for Modifications of Classical Orthogonal Polynomials,” Habilitation Thesis, University of Kassel, Kassel, January 2006.
[2] E. Keogh, S. Chu, D. Hart, and M. Pazzani, “An Online Algorithm for Segmenting Time Series,” Proc. IEEE Int’l Conf. Data Mining, pp. 289-296, 2001. [3] E. Keogh, S. Chu, D. Hart, and M. Pazzani, “Segmenting Time Series: A Survey and Novel Approach,” Data mining in time series databases 57,2004. [4] Erich Fuchs, Thiemo Gruber, Jiri Nitschke, and Bernhard Sick,”Online Segmentation of Time Series Based on Polynomial Least-Squares Approximations,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 32, No. 12, pp.2232-2245, December 2010. [5] W. Gautschi, G.H. Golub, and G.Opfer, “Applications and Computation of Orthogonal Polynomials,” Conference in Oberwolfach, pp.102-105, March 22-28, 1998. [6] M. Last, A. Kandel, and H. Bunke, eds., “Data Mining in Time Series Databases”, vol. 57, World Scientific Publishing, pp.1-22, 2004. [7] Y.I. Abramovich, N.K. Spencer, and M.D.E. Turley, “Time-varying autoregressive (TVAR) models for multiple radar observations,” IEEE Transactions on Signal Processing, Vol. 55, No. 4, pp.1298–1311, April 2007. [8] R.B. Pachori, and P. Sircar, “EEG signal analysis using FB expansion and second-order linear TVAR process,” Signal Processing, Vol 88, No.2, pp. 415–420 , 2008. [9] Matthias Arnold, * Wolfgang H. R. Miltner, Herbert Witte, Reinhard Bauer, and Christoph Braun, “Adaptive AR Modeling of Nonstationary Time Series by Means of Kalman Filtering,” IEEE Transactions on Biomedical Engineering, Vol. 45, NO. 5, May 1998. [10] Rui Zou, Heng Liang Wang, and Ki H. Chon, “A Robust Time-Varying Identification Algorithm Using Basis Functions, ” Annals of Biomedical Engineering, Vol. 31, pp. 840–853, 2003. [11] Luis David Avenda˜no Valencia,” Parametric Time–Frequency Analysis for Discrimination of Non–Stationary Signals,” M.S. thesis, Control and Digital Signal Processing Group Department of Electric and Electronic Engineering Universidad Nacional de Colombia , Manizales Colombia, May 2009. [12] Z.G. Zhang, H.T. Liu, S.C. Chan, K.D.K. Luk, and Y. Hua,*,” Time-dependent power spectral density estimation of surface electromyography during isometric muscle contraction: Methods and comparisons,” Journal of Electromyography and Kinesiology, pp.89-101, 2010. [13] Zbigniew Leonowicz, Juha Karvanen, Toshihisa Tanaka, and Jacek Rezmer, “Model order selection criteria: comparative study and applications,” International Workshop “Computational Problems of Electrical Engineering', Zakopane, 2004. [14] R. W. Schafer, “What is a Savitzky-Golay filter,” IEEE Signal Process. Mag., Vol. 28, No. 4, pp. 111–117, July 2011. [15] Jianwen Luo, Kui Ying, Ping He, and Jing Bai, “Properties of Savitzky–Golay digital differentiators,” Digital Signal Processing, Vol.15, pp. 122–136, 2005. [16] Dali Chen, Yang Quan Chen, and Dingyu Xue, ’’Digital Fractional Order Savitzky-Golay Differentiator,’’ IEEE Transactions on Circuits and Systems- II :Express Briefs, Vol. 58, No. 11, November 2011. [17] Timoor A. Sakharuk, “Computation of weighting functions for smoothing two-dimensional data by local polynomial approximation techniques,” Analyrrca Chlmrcu Acra, pp.331-336, 1991. [18] Dali Chen, Ding-Yu Xue, and Yang Quan Chen, “Digital Fractional Order Savitzky-Golay Differentiator and its application,” in Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Washington, DC, USA, August 28-31, 2011. [19] John B. Schneider, “Understanding the FDTD Method” , 2011, http://www.eecs.wsu.edu/~schneidj/ufdtd/ [20] S. Osher and J. Sethian, “Fronts propagating with curvature speed: Algorithms based on Hamilton-Jacobi formulations.” Journal of Computational Physics, Vol. 79, pp.12–49, 1988. [21] Aly A. Farag and M. Sabry Hassouna, “Theoretical Foundations of Tracking Monotonically Advancing Fronts Using Fast Marching Level Set Method,” Computer Vision and Image Processing Laboratory, University of Louisville, Louisville, Kentucky, Tech. Rep., February, 2005. [22] Rouy, E. and Tourin, A., SIAM J. Num. Anal. 29, pp.867-884, 1992. [23] Mustafa Cakir and Levent Sevgi, “Path Planning and Image Segmentation Using the FDTD Method,” IEEE Antennas and Propagation Magazine, Vol. 53, No. 2, April 2011. [24] J.A. Sethian , “Level Set Techniques for Tracking Interfaces; Fast Algorithms, Multiple Regions, Grid Generation, and Shape/Character Recognition ,” Dept. of Mathematics, University of California Berkeley, California. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65454 | - |
| dc.description.abstract | 在這篇碩士論文中，主要著重於離散正交多項式於訊號及影像處理的應用。這些應用概括了：時間序列的逼近與分段、時變自相關隨機程序模型的建立以及實作Savitzky-Golay濾波器並將其應用於訊號與影像處理。最後介紹了時域有限差分法(Finite Difference Time Domain)這個數值方法與其在路徑搜尋上的應用。
在架構上，首先，我會先介紹離散正交多項式的定義以及常見性質，並以其為基底函數應用於時間序列的逼近以及分段，且進一步地發展可快速求出基底函數權重的方法。接著同樣利用了正交多項式做為基底函數求取時變自相關隨機程序模型的參數以及實現Savitzky-Golay濾波器。其中對於Savitzky-Golay濾波器的性質與相關應用有較詳盡的整理，包含數位差分器、影像強化以及去除影像雜訊等等。並提出利用Savitzky-Golay濾波器的概念達到可兼顧影像品質以及雜訊強度的多重規模自適性除影像雜訊的方法。 希望這本論文能對您有幫助。 | zh_TW |
| dc.description.abstract | In this thesis, we mainly focus on the applications of discrete orthogonal polynomials, including time series approximation and segmentation, build of time-variant autoregressive (TVAR) process model and implementation of Savitzky-Golay filter (S-G filter) for image and signal processing. Besides, I also introduce the Finite difference time domain (FDTD) method, a numerical method used for solving electromagnetic wave equation originally, and its applications to path planning and image segmentation.
About the structure of this thesis, first, the definition and common properties of discrete orthogonal polynomials are introduced. Then using discrete orthogonal polynomials as bases, we apply them for time series approximation and segmentation with new developed fast update equation of weighting coefficients, estimation of parameters of time-variant autoregressive model and realization of Savitzky-Golay smoothing filter. Also, I summary the main applications and properties of Savitzky-Golay filter, such as digital differentiator, image enhancement and image denoising. I further proposed the multi-scale adaptive image denosing method based on the concept of Savitzky-Golay filter. Compared with traditional image denosing using Savitzky-Golay filter, the proposed method can maintain the detail of image better when denosing. May this thesis will be useful for you. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T23:44:08Z (GMT). No. of bitstreams: 1 ntu-101-R99942141-1.pdf: 6215611 bytes, checksum: 1da224452aeaa4def1e21f19ab37bf67 (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 誌謝………………… .i
中文摘要……… iii ABSTRACT… v CONTENTS… vii LIST OF FIGURES x LIST OF TABLES xiii Chapter 1 Introduction 1 Chapter 2 Discrete Orthogonal Polynomial and Its Application to Time Series Segmentation ……………………………………………………………4 2.1 Introduction to Time Series Segmentation 4 2.2 Least Square Errors Problem 5 2.3 Piecewise Polynomial Approximation 6 2.3.1 Moving Time Window Segmentation Using Orthogonal Polynomials 7 2.3.2 Restriction on Fast Update Procedure of Moving Time Window Approximation Using Orthogonal Polynomials 9 2.3.3 Proposed Growing Window Method for Online Segmentation Using Laguerre Polynomial 13 Chapter 3 Discrete Orthogonal Polynomial and Its Application to Time Variant Autoregressive Model Parameter Estimation 17 3.1 Introduction to Time-Varying Autoregressive Model 17 3.2 Estimation of Time Varying Autoregressive Model Parameters 19 3.2.1 Locally Stationary Method 19 3.2.2 Adaptive Methods 20 3.2.3 Basis Expansion Method 21 3.2.4 Proposed Basis Expansion with Recursive Computation Method 23 3.3 The Application of Time Varying Autoregressive Model to Noisy Image 28 3.3.1 Noisy Image 28 3.3.2 Time Varying Autoregressive Model on Image Representation 29 3.3.3 Comparison of Reconstructed Noisy Image Using Time Varying Autoregressive model and Polynomial Approximation Method 32 Chapter 4 Savitzky-Golay Filter and Its Applications 34 4.1 Introduction to Savitzky-Golay Filter 34 4.2 Relationship Between Online Time Series Approximation and Savitzky-Golay Filter 38 4.3 Fast Update Equation of Smoothing Process Coefficients 43 4.4 Application of Savitzky-Golay Filter to Digital Integer and Fractional Order Differentiator 45 4.5 Applications of Savitzky-Golay Filter to Image Processing 50 4.5.1 Image Denoising Using Savitzky-Golay Filter 50 4.5.2 Edge Detection Using Savitzky-Golay Differentiator 57 4.5.3 Image Enhancement Using Digital Fractional Order Savitzky-Golay Differentiator 60 4.5.4 Proposed Adaptive Image Denoising Using Savitzky-Golay Filter 68 Chapter 5 The Applications Using Finite Difference Time Domain Method 76 5.1 Introduction to Finite Difference Time Domain Method and Level Set Method 76 5.2 Distance Transform 82 5.3 Path Planning and Image Segmentation Using Finite Difference Time Domain Method 86 Chapter 6 Conclusion and Discussion 89 Reference 90 | |
| dc.language.iso | en | |
| dc.subject | 時間序列分段 | zh_TW |
| dc.subject | 離散正交多項式 | zh_TW |
| dc.subject | Savitzky-Golay 濾波器 | zh_TW |
| dc.subject | 去除影像雜訊 | zh_TW |
| dc.subject | Discrete orthogonal polynomial | en |
| dc.subject | Time series segmentation | en |
| dc.subject | Savitzky-Golay filter | en |
| dc.subject | Image denoising | en |
| dc.title | 離散正交多項式於訊號及影像處理的應用 | zh_TW |
| dc.title | Discrete Orthogonal Polynomial and Its Applications to Signal and Image Processing | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 祈忠勇(Chong-Yung Chi),徐忠枝(Jong-Jy Shyu) | |
| dc.subject.keyword | 離散正交多項式,時間序列分段,Savitzky-Golay 濾波器,去除影像雜訊, | zh_TW |
| dc.subject.keyword | Discrete orthogonal polynomial,Time series segmentation,Savitzky-Golay filter,Image denoising, | en |
| dc.relation.page | 92 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-07-24 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 電信工程學研究所 | zh_TW |
| 顯示於系所單位： | 電信工程學研究所 | |
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