首先，本論文研究一個為波松模型的隨機污染薄膜。在這個模型中，隨機薄膜上的污點被假設呈波松分佈(Poisson-distribution)，且污點具有重疊的性質，透射率的效應為乘積性。薄膜之自相關函數計算，將可由污點的濃度、半徑、透射率三個參數來獲得。這個自相關函數將被應用在還原天文望眼鏡所拍攝的影像。而這類影像信號通常在大氣的傳播過程中，遭受隨機分散的破壞。

影像還原時，本論文將使用三種不同的方法，來估測得三個關鍵的參數。他們分別是EM(expectation- maximization)演算法，及兩種依據不同定義方式的最大熵(Maximum-Entropy)法。還原效果是成功的，並且展示在這份論文中。

First, we study a Poisson model a polluted random screen. In this model, the defects on random screen are assumed Poisson-distribution and overlapped. The transmittance effects of overlapping defects are multiplicative. We can compute the autocorrelation function of the screen is obtained by defects' density, radius, and transmittance. Using the autocorrelation function, we then restore the telescope astronomy images. These image signals are generally degraded by their propagation through the random scattering in atmosphere.

To restore the images, we estimate the three key parameters by three methods. They are expectation- maximization (EM) method and two Maximum-Entropy (ME) methods according to two different definitions. The restoration are successful and demonstrated in this thesis.

第1章 前言 1
第2章 光學影像系統之基礎 3
2.1 傅氏光學 3
2.2 同調之影像系統 7
2.3 非同調之影像系統 9
2.4 同調轉移函數與OTF之間的關係 11
第3章 自相關函數的推論 13
3.1 透射雜訊 13
3.2 污染薄膜之統計自相關函數公式推導 14
第4章 影像還原的方法 20
4.1 EM演算法 20
4.2 反函數法 30
4.2.1 EM algorithm評分方式 31
4.2.2 第一型ME評分方式 33
4.2.3 第二型ME評分方式 34
第5章 實驗結果分析 36
5.1 樣本一:NGC7009 37
5.2 樣本二:NGC1300 39
5.3 樣本三:M51 41
第6章 結論 43
附錄一 45
附錄二 60
附錄三 64
參考文獻 66

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