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研究生： 梁瑋哲
Wei-Che Liang
論文名稱： Data adaptive median filters for image denoising based on a prediction criterion
指導教授： 陳春樹
Chun-Shu Chen
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 68
中文關鍵詞： 自由度 、中位數濾波法 、均方預測誤差 、空間預測
外文關鍵詞： degrees of freedom, median filter, mean squared prediction error, spatial prediction
相關次數： 點閱：12  下載：0 
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    • 中位數濾波法已被廣泛應用於影像的除噪議題。然而，使用中位數濾波法的關鍵在於必須先決定除噪的視窗大小。在本篇論文中，我們嘗試從抽樣點的資訊出發，利用空間克利金模型重建原始影像。基於預測的觀點，我們利用廣義Stein不偏風險估計法建立均方預測誤差的估計式，然後發展一種資料適應性的準則去決定合適的除噪視窗，進而重建背後真實的影像。透過各式的數據分析結果顯示，我們所提出的方法能較其它方法有更佳的影像重建結果。

    Median filter has been a popular technique for image restoration. An important issue of applying median filter is the choice of the span parameter in practice. In this thesis, we develop a data adaptive criterion to select the span parameter from a prediction perspective. Our proposed criterion is derived from the generalized Stein’s unbiased risk estimator (GSURE) and then the consequent criterion, an estimator of mean square prediction errors under a given span parameter, is established. According to the proposed criterion, an appropriate span is determined for the median filter method in the spatial model version to restore the underlying images. Comprehensive numerical results show that the proposed method is superior to its competitors.

    摘要 i Abstract ii 致謝辭 iii Contents iv Figure contents v Table contents vii 1. Introduction 1 2. Geostatistical models 3 2.1 Model settings 3 2.2 Spatial prediction and parameter estimation 4 3. Proposed methodology 8 3.1 Median filter 8 3.2 Span selection using GSURE 9 3.3 Modeling with a fixed effect model 13 3.4 Algorithms 16 4. Numerical results 18 4.1 Setup 18 4.2 Results for GSURE criterion 18 4.3 Results for spatial prediction 38 5. Conclusions and discussions 55 References 56

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