利用兩段式濾波器回復受脈衝和高斯混合雜訊干擾之影像

Abstract

在很多實際的系統中，由於感測器和傳輸頻道並不完美，而產生了雜訊。由於雜訊的存在，使得系統的輸出品質大大的受到影響，因此雜訊的移除是必須且重要的。本文著重在影像雜訊的去除，這裡所討論的雜訊主要是脈衝與高斯分佈或兼含兩者之雜訊。以往的濾波器是往往是用來處理某種單一類型雜訊，但是通常雜訊是以混合的方式存在，也就是同時含有上述兩種的雜訊，因此當混合式雜訊存在時，這時先前設計應付一種類型雜訊的濾波器將無法達到所需的要求。不同以往的濾波器設計，我們提出一套利用兩段式濾波器來處理上述兩種雜訊的方法。首先我們先偵測影像像素是否為脈衝雜訊所污染，如果是受到雜訊干擾，則用模糊分類的新型中值濾波器來加以處理，這樣能避免誤處理原始像素。然後將已經由第一級濾波器處理過後的影像，再由基於模糊規則(fuzzy rule-based)，簡稱FRB濾波器去除剩下的主要含高斯雜訊部分。此濾波器是一種權重平均的輸出，其設計是基於三個影響系統輸出的參數:像素間灰階值的差距，像素間的距離、方向，以及處理區域之像素間的變異性。經由最小的平均誤差平方(LMS)演算法，我們可以得到此濾波器的歸屬(權重)函數。 從實際應用面考慮，我們嘗試設計出一個依高斯雜訊程度而變之通用型FRB濾波器，適用於各種影像具有相同高斯雜訊程度的消除；依照我們所提出一套估測高斯雜訊程度的方法，去測定第一級處理後之影像高斯雜訊干擾程度，來選擇合適的通用型FRB濾波器，在進行第二級之高斯雜訊消除。最後由實驗結果我們可以證明我們所提出的兩段式濾波方法在影像雜訊移除的效果及其強健性。

In many practical image systems, noise causes from the imperfection of the sensors and communication channels, and the output of the system are greatly affected by the existence of the noise. Therefore, it is necessary and important to remove the noise. The thesis introduces several schemes for the image noise removal; including the impulse and Gaussian noise distribution, and both. Most filters were designed to process single noise type, however, a mixed noise contamination of images often is observed in a practical system. When the noise appears in mixed mode, the single noise type filters cannot facilitate an effective filtering action. Differently, we propose a two-stage filter that can remove the noise mixed with impulse and Gaussian noise from an image. First, we detect the image pixel to check whether the image pixel is impulse noise contaminated or not. If the pixel is corrupted by the impulse noise, a new fuzzy classified augmented median filter is applied to replace only the noisy pixel, which will prevent us from destroing the original image structure. Then the processed image is filtered by the use of the fuzzy rule-based (FRB) filter to remove the remaining noise, whose noise contains Gaussian type mostly. The output of the fuzzy rule-based filter is a weighted average of the current processing pixel and its neighborhood pixels. The design of the FRB filter is based on three parameters: the gray level difference between pixels, the spatial distance and direction between pixels, and the variance in the local window. Using the LMS learning algorithm, we can obtain the membership function for the filter. Moreover, from a practical consideration, we try to design a Gaussian noise dependent universal filter, which can be used for all kinds of images to filter the Gaussian noise of corresponding level. Via the proposed Gaussian noise level estimation algorithm, the remaining Gaussian noise variance of the first-stage processed noisy image can be obtained and the appropriate universal FRB filter can then exploited for the second-stage filter action. From the simulation results, our proposal two-stage filtering scheme has demonstrated the effectiveness and robustness, in comparison with other filters in image noise removal.