在日常生活中，照片的保存極為不易；甚至若是照片長期暴露在充滿塵埃的空氣中，更是容易受到塵埃的污染而破壞照片的本質。本篇論文的研究即將受到污染的圖像去估測污點於其上之分佈情形，進而分析受污染圖像、未受污染圖像與雜訊三者間的自相關函數之關係，斬獲近似於未受污染圖像之自相關函數；再者，利用自相關函數之特性來還原出近似於未受污染的圖像。
而在本篇論文的成像系統中，是將受污染的圖像視為包含著含有透射雜訊（transmittance noise）之薄的隨機介質面；在此介質面上，污點是呈波松分佈（Poisson distribution），具重疊的性質，且其透射率效應是乘積性（multiplicative）的。藉此，我們可以分析出雜訊的統計自相關函數。然而，在計算圖像的程序自相關函數時，必須將圖像視為具週期性的信號，以避免計算時資料不足的現象。
關於受雜訊的污染圖，我們是採用電腦模擬的方式獲得；將此模擬出的受污染圖用此研究方法來執行影像還原的工作，我們不難發現，雜訊的效應確實減少了許多。

It’s not easy to keep photographs clean in every day. A photograph is liable to be polluted by accumulating defects such as dusts, which can degrade the imaging quality. In the thesis, a method of image restoration is proposed for image polluted by multiplicative transmittance noise. The method is based on estimating the approximate autocorrelation function of the unpolluted image. This autocorrelation function is obtained by analyzing the relationship among the autocorrelation function for polluted image, unpolluted image and noise. Further more, the noisy image is restored by the property of the autocorrelation function.

A polluted photograph in imaging system is modeled by a thin random screen against the original image. In this model, defects are Poisson-distribution and may be overlapped. Since transmittance effect of each defect is multiplicative, the transmittance of random screen is computed as a product of Poisson-distribution-centered random function. Then, the statistical autocorrelation function of random screen is accordingly computed. More specifically, we should rearrange image data as periodic signal to avoid insufficient data in computing the process autocorrelation function.

The simulated polluted image is restored by the amplitude information from the estimated autocorrelation function of the original image. Simulating results is demonstrated that the RMS of the restored image computed with the polluted image is improved.

第一章 引言

第二章 污染薄膜的模式
2.1 本章概敘
2.2 棋盤模式
2.3 重疊圓粒模式
2.4 透射雜訊模式
2.4-1 透射雜訊

第三章 透射雜訊的統計性質
3.1 本章概敘
3.2 透射雜訊之自相關函數
3.2.1 自相關函數之公式推導
3.3 數值結果

第四章 透射雜訊的生成模擬
4.1 本章概敘
4.2 均勻變異數
4.2.1 其他種類的變異數
4.3 模擬實驗的程序
4.3-1 模擬結果

第五章 利用透射雜訊的影像還原
5.1 本章概敘
5.2 影像還原方法之討論
5.3 還原結果與分析


第六章 結論

[1] J.W. Goodman,〝Statistical Optics〞,A Wiley-Interscience Publication Wiley & Sonc Co. New York（1985）,Chapter 8.

[2]E. L. O’Neill,〝Introduction to Statistical Optics〞,Addison-Wesley,Reading,MA（1963）,
Chapter 8.

[3]B. S. Chow,〝Transmittance Noise：A new model of thin random medium for optical image system〞
,Proceeding Telecommunication,pp 455-460,1989.

[4]Reuven Y. Rubinsten,1981,〝Simulation and Monte Carlo methods〞,John Wiley & Sons,Inc.,
Chapter 2.

[5]Reuven Y. Rubinsten,1981,〝Simulation and Monte Carlo methods〞,John Wiley & Sons,Inc.,
Chapter 3.

[6]William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling,1992,〝Numerical Recipes in C：The Art of Science Computing〞,
Cambridge University Press,Chapter 7.

[7]William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling,1992,〝Numerical Recipes in C：The Art of Science Computing〞,
Cambridge University Press,Chapter 12.

[8]W. K. Pratt,〝Digital Image Processing〞,Wiley-Interscience,New York,1991.

[9]A. K. Jain,〝Fundamentals of Digital Image Processing〞,New York, Prentice-Hall Inc.,1989.

[10]Rafael C. Gonzalez, Richard E. Wood,〝Digital Image Processing〞,Addison-Wesley Inc.,1992.

[11]R. E. Ziemer,W. H. Tranter, 〝Principles of Communication：Systems, Modulation, and Noise〞, Houghton Mifflin Co., Boston,1995.