The image's restoration is an essential step in medical imaging. Several Filters are developped to remove noise, the most interesting are filters who permits to denoise the image preserving semantically important structures. One class of recent adaptive denoising methods is the nonlinear Partial Differential Equations who knows currently a significant success. This work deals with mathematical study for a proposed nonlinear evolution partial differential equation for image processing. The existence and the uniqueness of the solution are established. Using a finite differences method we experiment the validity of the proposed model and we illustrate the efficiently of the method using some medical images. The Signal to Noise Ration (SNR) number is used to estimate the quality of the restored images.