To limit the noise in an image, some techniques are based on the calculation of an average intensity in each pixel of the image by considering a some neighbor. However, these techniques tend to attenuate contours present in the image. This affect edge and particularly penalizing for the segmentation algorithms whose finality is to find contours. The restoration method by minimization of total variation, suggested by Rudin et al. (1992), consists in minimizing under constraints of the great variations present in the image while preserving contours. In this paper, we propose an adaptation of the method of Rudin et al. (1992) to the ultrasound images restoration.