貝蘇章臺灣大學:電信工程學研究所陳佩君Chen, Pei-JiunPei-JiunChen2010-07-012018-07-052010-07-012018-07-052009U0001-1006200915515900http://ntur.lib.ntu.edu.tw//handle/246246/188345此論文主要為討論局部多項式近似法又稱局部多項式迴歸，於影像處理之應用。局部多項式近似法主要運用於訊號回復。二章將介紹局部多項式近似法觀測訊號之模型及權重視窗大小的選擇。並解釋如何運用多項式近似法來合成和恢復訊號。權重視窗的頻寬在訊號近似準確度中扮演很重要的角色。為了求出理想的視窗寬度，我們運用統計學上方法—信賴區間。於相對上比較複雜的影像訊號，使用具方向性的視窗能保留更多影像的細節。第四章中介紹的非等方向性的LPA-ICI kernel即是具方向性的視窗的一種。五章將介紹局部多項式近似法應用於時頻分析。部多項式近似法於影像處理之應用則留到論文的最後一章，包括去雜訊、去模糊、及彩色濾鏡陣列。The main idea of this thesis is to discuss local polynomial approximation (LPA) employed in image processing. It is also called local polynomial regression. LPA is used to reconstruct signals.n Chapter 2, the observation model of LPA is introduced, and so is the basis weighting window. How it is applied to signal synthesis and reconstruction is also explained here. The bandwidth of weighting window plays an important role in the accuracy of signal estimation. In order to find the ideal window size, we employ a statistical technique, intersection of confidence intervals (ICI).or relatively complex image signals, using directional windows can reserve more details of the image. The anisotropic LPA-ICI kernel in Chapter 4 is one of the directional windows.he time-frequency transform using LPA is briefly introduced in Chapter 5. pplications of Local Polynomial Approximation technique in image processing are in the last Chapter, including denoising, deblurring, and color filter array (CFA).口試委員會審定書 #謝 i文摘要 iiBSTRACT iiiONTENTS ivIST OF FIGURES viiIST OF TABLES ixhapter 1 Introduction 1.1 Local Polynomial Approximation 1.2 Adaptive Scale Selection 2hapter 2 Local Polynomial Approximation 5.1 Basis of Local Polynomial Approximation 5.1.1 Idea of Local Polynomial Approximation 5.1.2 Weighting Window 9.1.3 Estimate Calculation 12.2 Kernel LPA Estimates 16.2.1 Estimation of Signal 16.2.2 Estimation of Derivative 17.2.3 Reproducing Polynomial Kernels 18.3 Nonparametric Regression 23.3.1 Regression function 23.3.2 Nadaraya-Watson estimate 24.3.3 LPA estimate 24.4 Shift-Invariant Kernels 25hapter 3 Adaptive Scale Selection 30.1 Discrete LPA Accuracy 30.1.1 Estimation Errors 30.1.2 Variance 31.1.3 Bias 31.2 Scale 34.2.1 Variant Scale 34.2.2 Invariant Scale 39.3 Intersection of Confidence Intervals 41.3.1 LPA-ICI Algorithm 41.3.2 Complexity and Convergence 48.3.3 Threshold Adjustment 49.4 Example: 1-D De-noising 49hapter 4 Anisotropic LPA-ICI 53.1 Directional LPA 53.1.1 Polynomials 53.1.2 Directional Windowing and Rotation 54.1.3 Calculations 55.1.4 Shift-invariant Kernels 56.2 Accuracy Analysis 58.2.1 Polynomial 58.2.2 Basic Estimates 61.2.3 Rotated Estimates 65.3 Adaptive Scale 70.3.1 Scale Setting 70.3.2 Estimates and Estimates Fusion 70.3.3 Complexity 71hapter 5 Local Polynomial Fourier Transform 72.1 Time-Frequency Transform 72.2 Local Polynomial Time-Frequency Transform 73hapter 6 Applications in Image Processing 75.1 Image Denoising 75.1.1 Example I: Cameraman 256x256 75.1.2 Example II: Lena 512x512 77.1.3 Example: III: Different Anisotropism 78.2 Image Deblurring 82.2.1 Example I: Cameraman 256x256 with BSNR 25dB 82.2.2 Example II: Camera man 256x256 with BSNR 40dB 84.3 Color Filter Array 87.3.1 Example I: Kodak 01 89.3.2 Example II: Kodak 05 91.3.3 Example III: Kodak 07 93hapter 7 Conclusions and Future Work 95EFERENCE 965866049 bytesapplication/pdfen-US局部多項式近似影像處理localpolynomial approximationregressionimage processingthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/188345/1/ntu-98-R96942105-1.pdf