Non-linear or anisotropic regularization PDE's (Partial Differential Equation) raised a strong interest in the field of medical image processing. The benefit of PDE-based regularization methods lies in the ability to smooth data in a nonlinear way, allowing the preservation of important image features (contours, corners or other discontinuities). In this article, we propose a PDE-based method restoration approach integrating a double-well potential as diffusive function. It is shown that this particular potential leads to a particular regularization PDE which makes the integration of prior knowledge about the gradient intensity level to enhance possible. The corresponding method shows interesting properties regarding stability and preservation of fine structures. As a proof a feasibility, results of restoration are presented on natural images to show potentialities of the proposed method. We also address a particular medical application: enhancement of tagged cardiac MRI.