Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics

Image restoration refers to the problem of removal or reduction of degradation in blurred noisy image. The image degradation is usually modeled by a linear blur and an additive white noise process. The linear blur involved is always an ill-conditioned which makes image restoration problem an ill-posed problem for which the solutions are unstable. Procedures adopted to stabilize the inversion of ill-posed problem are called regularization, so the se- lection of regularization parameter is very important to the e{uFB00}ect of image restoration. In this thesis, we study some numerical methods for solving this ill-posed problem. Dynamical systems method (DSM), Tikhonov regularization method, L-curve method, and generalized cross validation (GCV) method are introduced for solving this ill-posed problem. Some test examples and comparative studies are presented. From the numerical results, we can con- clude that DSM showed improved restored images compared to L-curve method and GCV method. Parts of this thesis were published in International Journal Mathematical Sciences Letters, 2015 [143]. Also, parts of this thesis were presented in 3rd Inter- national Conference on Mathematics and Information Science (ICMIS 2013), Luxor, Egypt, 28-30 Dec. 2013.

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