在光學成像系統中透鏡是一個很重要的元件，不過透鏡容易受到污染而變成有缺陷，造成成像品質的下降。被污染的透鏡可以等效成一張隨機的污染薄膜緊靠著乾淨的透鏡。在我們的模型中,污染薄膜上的污點假設呈波松分布(poison-distribution)，具重疊的性質，且其透射率效應是乘積性的。我們將應用卡門濾波器來估測污染透鏡成像系統的光學轉換函數。實驗中我們所用到的儀器有影像攝影機,影像擷取卡,個人電腦。

卡門濾波器定義兩個模式來解決估測上的問題：這兩個模式分別是訊號模式和觀察模式。卡門濾波器原本是被用在最佳估測領域中的控制和追蹤。近來，卡門濾波器常常被應用在影像還原的問題中。在本論文中，訊號模式是污點和乾淨圖的比值。在觀察模式中，加成雜訊來自於電子元件的取樣。實驗結果證實對於影像還原，估測光學轉移函數是有用的。

The lenses are important elements in optical imaging systems. However, lenses are liable to defects such as dusts and thus deteriorate their imaging quality. The polluted lens can be verified equivalent to a polluted random screen set against a clean lens. In our model, the defects on random screen are assumed poison-distribution, overlapped and the transmittance effect of each defect is multiplicative. In this thesis, we will apply Kalman filter to estimate the optical transfer function for a defected imaging system. The experiments are set up by the instruments including the video camera, capture card, and personal computer.

Kalman filter addresses an estimation problem defined by two models: the signal model and the observation model. Kalman filter was originally developed in the field of optimal estimation for application of controlling and tracking. Recently Kalman filter has been very often applied to the problems of image restoration. In this thesis, the signal model is obtained from a ratio of the defected and clean pictures in frequency domain. The observation model is built for an additive measurement noise from electronic sampling. Experimental results 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 5
2.1 同調之影像系統 5
2.2 非同調之影像系統 7
2.3 同調轉移函數與OTF之間的關係 9
第3章 卡門濾波器 10
3.1 卡門濾波器簡介 10
3.2 一維卡門濾波 10
3.3 二維卡門濾波器 13
3.4 減少更新(REDUCE UPDATE)卡門濾波器 25
3.5 應用區域參數於卡門濾波器 28
3.5.1 簡介 28
3.5.2 灰階影像分割 29
3.5.3 區域參數及卡門濾波器的配合 34
第4章 自相關函數 51
4.1 透射雜訊 51
4.2 自相關函數之期望值 52
4.3 污染透鏡OTF 之期望值 57
4.4 自相關的估測與熱雜訊的影響 59
第5章 實驗及分析 67
5.1 實驗的模型 67
5.2 影像還原 68
5.3 消除熱雜訊對自相關函數的影響 69
第6章 結論 75
附錄 76
參考文獻 85

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