利用模糊加權平均集成運算於影像脈衝雜訊去除

Abstract

在本論文中，我們提出以模糊加權平均集成運算的演算法去除影像中的脈衝雜訊，我們利用模糊加權平均集成運算建立區間值模糊關係進行灰階影像雜訊點偵測。為此，我們使用兩個加權參數，對整張影像以 視窗內中心像素和其八鄰域像素進行加權平均集成運算，計算中心點與鄰點之加權平均差植，再經由門檻值作用後，進而判斷中心像素是否為雜訊點。此外，為了減少誤判個數，我們在訓練階段中針對加權參數與門檻值推導出一套遞迴反覆的學習機制，最後我們將口袋演算法嵌入至學習機制中，藉此訓練出最佳的加權參數與門檻值，讓非雜訊點與雜訊點的誤判個數能夠最小化。 測試階段分為3個步驟：影像直方圖統計、雜訊點偵測、影像修復。首先我們先計算測試影像直方圖並找出可能的雜訊點群。接著，針對這些可能的雜訊點群，我們使用訓練階段所得的最佳參數進行雙重檢驗，偵測此點是否為雜訊點。一旦像素點被判為雜訊點時，此點將會被加權平均濾波器所修復。成果顯示，我們所提出的方法，其修復結果與現有的演算法結果相比，我們的方法更能有效的濾除影像中的脈衝雜訊，並且保留更多影像細節。此外，針對含有97% 的高強度雜訊影像，我們的方法也能夠將其恢復至一定程度的原始影像。

In this thesis, we propose a fuzzy weighted mean aggregation algorithm for denoising images corrupted by low or high-intensity impulse noise. We utilize fuzzy weighted mean aggregation algorithm to construct Interval-Valued Fuzzy Relations (IVFR) for grayscale image noise detection. To this end, we use two weighting parameters to calculate the weighted mean difference of the central pixel and its 8-neighborhood pixels in a sliding window across the image. Then, the central pixel will be identified as noisy or noise free by using a threshold operation. Besides, to decrease the noise detection error, we have derived the iterative learning mechanism of these weighting parameters of the mean aggregation and thresholds in the training stage. Finally, we embed the pocket algorithm in our learning mechanism to train the best parameter set to minimize the noisy and noise free pixel detection error. In the testing stage, we propose a new filtering method. It is divided into three steps: image histogram, noise detection, and image restoration. First, we calculate the histogram of the testing image to find the groups of potential noise pixels. On these possible noisy pixel groups, we make use of the best weighting parameters trained to perform the fuzzy weighted mean aggregation to double-check whether they are noise corrupted or not. If a pixel is identified as noisy, its value will be restored by a weighted mean filter. Simulation results show that the proposed algorithm provides a significant improvement over other existing filters and preserves more image details. Our algorithm can barely restore the image even when the noise rate is as high as 97%.