隨著科技不斷地發展，近年來在數位影像處理技術已提出了許多相關的新理論及新的演算法，人類也越來越重視數位影像的發展，為了滿足科技發展上的需求，影像處理技術就顯得相當重要。
　　影像復原主要是移除或改善導致影像惡化的原因，也就是將損壞的影像經過處理後而得到一個接近原理想影像的估計影像，而本文之研究主要是針對影像受到雜訊影響之問題來做探討。對於去除影像雜訊以改善影像品質，本研究主要是利用有限元素法將退化模型轉化為一大型線性系統，利用鄰域平均法與高斯核心法將受高斯雜訊干擾的影像模糊化後，再以推導出的二次模糊算子 、 及迭代演算法CGM(Conjugate gradient method)來求得線性系統之解，以達到去除高斯雜訊之效果，而實驗結果則以主觀式評定及定量式評定來做影像復原成效之比較。
　　最後，由實驗結果可知，高斯核心法在去除高斯雜訊所得到的成效較優於過去平滑化處理、中值法及鄰域平均法所得的結果。

　　As science and technology developed constantly in recent years, people put forward many related new theories and new algorithm in the digital image processing technique. Humanity also puts more and more emphasis on the development of the digital image. In order to satisfy the demand of technical development,the technique of image processing appears quite important.
　　The image restoration is mainly to remove or improve the cause of image depravation. In other words, image restoration is to process the impaired image and get an estimative image, which approximates the original image. The research in this content is mainly to aim at discussing the problem that the image is influenced by the noise. Regarding cleaning the image noise to improve the quality of image, this research is mainly using the finite element method to convert the degenerative model into a large linear system, making use of the neighborhood averaging method and the Gaussian kernel method to blur the image that is subjected to the Gaussian noise interference, and then solving the linear system by the reblurred operators and , and the conjugate gradient method, so that the Gaussian noise can be remove. The result of simulation is compared by subjective fidelity criterion and objective fidelity criterion.
　　From the result of simulation,the effect of using the Gaussian kernel method to remove the Gaussian noise is better than those of using the smoothing process, the standard median filter, and the neighborhood averaging method.

[1] Reinhard Klette and Piero Zamperoni, Handbook of Image Processing Op-
Erators.Wiley, 1996.
[2] Rafael C. Gonzalez and Paul Wintz, Digital Image Processing. Addition We-
sley, 1977.
[3] Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing. Addit-
ion Wesley, 1992.
[4] H.C. Andrews and B. R. Hunt, Digital Image Restoration. Prentice-Hall, 197
7.
[5] H. R. Schwarz, Finite Elemen Methods. Academic Press, 1988.
[6] Claes Johnson, Numerical solution of partial differential equations by
the finite element method. Cambridge University Press, 1987.
[7] David Kincaid and Ward Cheney, Numerical Analysis:Mathematics of Sci-
entific Computing. Brooks/Cole, 1991.
[8] A. E. Savakis and H. J. Trussell, “Blur identification by residual
spectral matching”, IEEE Trans. Image Proc., vol. 2, No. 2, pp. 252-259,
April 1993.
[9] H. J. Trussell , “Convergence criteria for iterative restoration
methods”,IEEE Trans. Acoust., Speech, and Signal Proc., vol. Assp-31,
No. 1, pp. 129-136, Feb. 1983.
[10] Rabab K. Ward, “Restoration of differently blurred versions of an image
with measurement errors in the PSF’s”, IEEE Trans. Image Proc., vol. 2,
No. 3, pp. 369-381, July 1993.
[11] Talal Rahman,Xue-Cheng Tai,Stanley Osher, “A TV-Stokes denoising
algorithm”,November 2006.
[12] 黃大川,侯世章指導, “迭代影像復原法則之數值探討”,國立成功大學應用數學所碩士論文,1994.
[13] 藍信傑,王中行指導, “以模糊理論為基礎之雜訊影像與分割臨界值的改善”,私立大葉大學自動化工程學系碩士班論文,2001.
[14] 林啟明,謝欣然指導, “應用模糊切換濾波器技術於影像脈衝式雜訊去除之研究”,國立東華大學電機工程學系碩士論文,2005.
[15] 黃文吉, C++ Builder與影像處理 ,儒林圖書公司發行,2005.