In this thesis, we have a comprehensive study of the famous compound Gauss-Markov image model. In this model, a pixel in the image random field is determined by the surrounding pixels according to a predetermined line field. This model is useful in image restoration by applying two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field. CGM (Compound Gauss-Markov) image modeling is characterized by the line fields and the generating noise. In this thesis we apply combinations of techniques such as changing processing order, immediate updating, probability determination and different methods to find the best modeling. Furthermore, the effects of the above modeling are demonstrated by its energy, visual quality, and error resistance. Finally, by solving a set of nonlinear equations we apply the CGM model to an image restoration problem for image corrupted by a dusted lens.