Kalman filter近年來被廣泛的使用在影像還原。在本篇論文中，我們應用卡門濾波器去為影像系統估測光學轉移函數。訊號模式為光學轉移函數，而光學轉移函數可由有汙點的圖與乾淨的圖在頻域上的比得到。

光學影像訊號的取樣會牽涉到熱雜訊。我們塑造熱雜訊為可加性的測量雜訊。我們藉Winner filtering去除熱雜訊。而被濾除熱雜訊的影像最後可由上述估測出的光學轉移函數還原。

在實驗需要的儀器包含錄影攝影機、擷取卡與個人電腦。實驗的結果包含了gamma參數與雜訊能量的估測，然而驗證光學轉移函數對於影像還原是有用的。

Recently Kalman filter has been well applied to the problems of image restoration. In this thesis, we apply Kalman filter to estimate the optical transfer function for an imaging system. The signal model is the optical transfer function obtained from a ratio of the defected and clean pictures in frequency domain.

There is thermal noise involved in sampling the optical image signal. We model this thermal noise as the additive measurement noise. We remove the thermal noise by Winner filtering. This filtered image is finally restored by the above estimated the optical transfer function.

The experiments are set up by the instruments including the video camera, capture card, and personal computer. Experimental results, including the estimation of gamma and noise power, have demonstrated that the estimated optical transfer function is useful for image restoration.

第1 章 引言 3
第2 章 光學影像系統之基礎 7
2.1 同調之影像系統 7
2.2 非同調之影像系統 9
2.3 同調轉移函數與OTF 之間的關係 11
第3 章 自相關函數 12
3.1 透射雜訊 12
3.2 自相關函數之期望值 13
3.3 污染透鏡OTF 之期望值 17
3.4 自相關的估測與熱雜訊的影響 20
第4 章 實驗結果與分析 29
4.1 實驗的模型 29
4.1.1 影像模式之真實影像，熱雜訊無含乘積雜訊 30
4.1.2 影像模式之真實影像( γ =1)，熱雜訊有含乘積雜訊 30
4.1.3 影像模式之想像影像( γ ≠ 1)，熱雜訊有含乘積雜訊 31
4.2 BISPECTRUM 32
4.3 影像還原 33
4.4 利用分割卡門去除熱雜訊 35
4.4.1 真實影像經分割卡門去熱雜訊(無含乘積雜訊) 35
4.4.2 真實影像經分割卡門去熱雜訊(有含乘積雜訊) 39
4.4.3 想像影像經分割卡門去熱雜訊(有含乘積雜訊) 41
4.5 消除自相關函數的熱雜訊及影像之還原 45
4.5.1 真實影像之還原， 熱雜訊無含乘積雜訊 46
4.5.2 真實影像之還原， 熱雜訊有含乘積雜訊 49
4.5.3 假想影像之還原熱雜訊有含乘積雜訊 52
第5 章 結論 56
附錄前言 57
附錄 58
參考文獻 82

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