Double Well Potential as Diffusive Function for PDE-based Scalar Image Restoration Method

Anisotropic regularization PDE’s (Partial Differential Equation) raised a strong interest in the field of 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 it possible integration of prior knowledge about the gradients intensity level to restore. As a proof a feasibility, results of restoration are presented both on ad hoc and natural images to show potentialities of the proposed method.