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.
