Images are liable to being corrupted by noise when they are processed for many applications such as sampling, storage and transmission. In this thesis, we propose a method of image restoration for image corrupted by a white Gaussian noise. This method is based upon Gauss-Markov random field model combined with a technique of image segmentation. As a result, the image can be restored by MAP estimation. In the approach of Gauss-Markov random field model, the image is restored by MAP estimation implemented by simulated annealing or deterministic search methods. By image segmentation, the region parameters and the power of generating noise can be obtained for every region. The above parameters are important for MAP estimation of the Gauss-Markov Random field model. As a summary, we first segment the image to find the important region parameters and then restore the image by MAP estimation with using the above region parameters. Finally, the intermediate image is restored again by the conventional Gauss-Markov random field model method. The advantage of our method is the clear edges by the first restoration and deblured images by the second restoration.

The restoration of degraded images is one important application of image processing. The classical approach of image restoration, such as low-pass filter method, is usually stressed on the numerical error but with a disadvantage in visual quality of blurred texture. Therefore, a new method of image restoration, based upon image model by Compound Gauss-Markov(CGM) Random Fields, using MAP(maximum a posteriori probability) approach focused on image texture effect has been proved to be helpful. However, the contour of the restored image and numerical error for the method is poor because the conventional CGM model uses fixed global parameters for the whole image. To improve these disadvantages, we adopt the adjustable parameters method to estimate model parameters and restore the image. But the parameter estimation for the CGM model is difficult since the CGM model has 80 interdependent parameters. Therefore, we first adopt the parameter reduction approach to reduce the complexity of parameter estimation. Finally, the initial value set of the parameters is important. The different initial value might produce different results. The experiment results show that the proposed method using adjustable parameters has good numerical error and visual quality than the conventional methods using fixed parameters.

This Compound Gauss-Markov image model has been proven helpful in image restoration. In this model, a pixel in the image random field is determined by the surrounding pixels according to a predetermined line field. In this thesis, we restored the noisy image based upon the traditional Compound Gauss-Markov image field without the constraint of the model parameters introduced in the original work. The image is restored in two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field. Two methods are proposed to replace the traditional method in solving for the line field. They are probability method and vector method. In probability method, we break away from the limitation of the energy function Vcl(L) and the mystical system parameters Ckll(m,n) and£mw2. In vector method, the line field appears more reasonable than the original method. The image restored by our methods has a similar visual quality but a better numerical value than the original method.