污染影像的還原是影像處理的一項重要的應用。古典的影像還原方法如權重平均的低通濾波器(Low-pass filter)，雖然數值誤差方面不錯，但其視覺效果卻不好，因為還原的影像紋理模糊。為了改善此現象便興起一種強調視覺效果的方法，其中以複合高斯馬可夫隨機場(Compound Gauss-Markov(CGM) Random Fields)來描述影像的方法最著稱，雖然還原的數值誤差不好，但卻大幅改善了紋理的視覺效果，然而影像的輪廓部份卻不明顯，這是因為傳統的複合高斯馬可夫隨機場還原法採用固定的模組參數還原影像，為了改善數值的誤差及輪廓部分，我們採用了新方法去估測參數，但參數的估測非常困難，因為有80個相依的參數，故我們採用參考文獻中的參數降階法將參數降至7個獨立的參數，然而為了速度及簡單的考量，其中5個變異數的參數部份我們採用文獻所提供的值，所以只估測兩個獨立參數，然而參數初始值及範圍的設定相當的重要，儘量使相對應之權值係數總和接近1，如此不但能減少收斂時間，且能得到好的還原效果。最後，傳統的複合高斯馬可夫隨機場還原法採用像素場及邊緣場的輪流更新，而我們的方法採用像素場、邊緣場及參數的輪流更新當然我們的方法能得到好的還原效果。

The restoration of degraded images is one important application of image processing. The classical approach of image restoration, such as low-pass filter method, is usually stressed on the numerical error but with a disadvantage in visual quality of blurred texture. Therefore, a new method of image restoration, based upon image model by Compound Gauss-Markov(CGM) Random Fields, using MAP(maximum a posteriori probability) approach focused on image texture effect has been proved to be helpful. However, the contour of the restored image and numerical error for the method is poor because the conventional CGM model uses fixed global parameters for the whole image. To improve these disadvantages, we adopt the adjustable parameters method to estimate model parameters and restore the image. But the parameter estimation for the CGM model is difficult since the CGM model has 80 interdependent parameters. Therefore, we first adopt the parameter reduction approach to reduce the complexity of parameter estimation. Finally, the initial value set of the parameters is important. The different initial value might produce different results. The experiment results show that the proposed method using adjustable parameters has good numerical error and visual quality than the conventional methods using fixed parameters.

目錄
第一章 緒言 1
第二章 複合高斯馬可夫隨機場理論之回顧 5
2.1 簡介 5
2.2 複合高斯馬可夫隨機場 5
2.3 聯合最大後置機率(MAP)估測 10
2.3.1決策搜尋法 13
第三章 複合高斯馬可夫模型之參數降階 16
3.1 簡介 16
3.2 參數降階 16
第四章 影像還原 24
4.1 簡介 24
4.2 參數估測與影像還原流程圖 24
4.2.1結合低通濾波器、區域成長分割與傳統複合高斯馬可夫隨機場還原法 25
4.2.2 變動參數型的複合高斯馬可夫隨機場還原法 25
第五章 實驗結果及比較 29
5.1 簡介 29
5.2 實驗結果 29
第六章 結論 50

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