Ultrasound images provide the clinician with non-invasive, low cost, and real-time images that can help them in diagnosis and plannnig and therapy. However, although the human eye is able to derive the meaningful information from these images, automatic processing is very difficult because of the noise and artefacts present in the image. In this work, we propose to extend the current anisotropic diffusion technique to deal with the speckle noise present in the Ultrasound images. To this end, we use a previously derived model of the noise, and we write the restoration scheme as a energy minization constrained by the noise model and parameters. This approach leads to a new data attachment term whose optimal weight can be automatically estimated. 1 This work was supported by CIMIT.