局部多項式近似法於影像處理之應用

Local Polynomial Approximation Technique in Image Processing

陳佩君(Pei-Jiun Chen)

指導教授 ： 貝蘇章

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.00665

摘要

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。
第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。
對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。
第五章將介紹局部多項式近似法應用於時頻分析。
局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。

關鍵字

局部 ； 多項式 ； 近似 ； 影像處理

並列摘要

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.
In 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).
For 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.
The time-frequency transform using LPA is briefly introduced in Chapter 5.
Applications of Local Polynomial Approximation technique in image processing are in the last Chapter, including denoising, deblurring, and color filter array (CFA).

並列關鍵字

local ； polynomial approximation ； regression ； image processing

參考文獻

[1] M. Unser, A. Aldroubi, M. Eden, “Polynomial Spline Signal Approximations: Filter Design and Asymptotic Equivalence with Shannon’s Sampling Theorem,” IEEE Trans. Information Theory, vol. 38, NO. 1, pp95-103, Jan. 1992.

[2] V. Katkovnik, “On Adaptive Local Polynomial Approximation with Varying Bandwidth, ” IEEE, pp2321-2324, 1998.

[3] V. Katkovnik, “A New Method for Varying Bandwidth Selection, ” IEEE Trans. Signal Processing, vol. 47, NO. 9, Sep. 1999.

[4] S. C. Chan and Z. Zhang, “Multi-Resolution Analysis of Non-Uniform Data with Jump Discontinuities and Impulse Noise Using Robust Local Polynomial Regression, ” IEEE ICASSP, II-pp769-772, 2004.

[5] S. C. Chan and Z. Zhang, “Robust Local Polynomial Regression with Adaptive Bandwidth, ” IEEE ISCAS, III-pp333-336, 2004.