Summary: Digital images are generally degraded by different sources during their acquisition. This is due of two types of phenomena: the deterministic phenomenon of blur which is introduced by relative motion between a camera and the object, and the stochastic phenomena such as atmospheric turbulence, noise and other factors. So, it becomes very difficult for high level processing systems (object detection, three-dimensional reconstruction, characters recognize \dots) to extract reliable features from the incomplete edges. Our objective is to reduce the effect of this degradation and recover the original image from the degraded image with better edge detection. The Markov random field modelization allows us to restore images with taking into account some constraints such as the smoothing constraint and the edge preserving. Our approach is focused on a new deterministic algorithm that permits approaching the global optimum and reduces computational time. We present the semi-quadratic regularization model adapted to discontinuities in order to model smoothing constraints of homogeneous zones land to preserve contours. The obtained results on real images are satisfying since we reached our goal of a smoothed homogeneous area with preserved edge.