Image restoration with surface-based fourth-order partial differential equation

Abstract

This paper presents an edge-preserving fourth order partial differential equation (PDE) for image restoration derived from a new surface-based energy functional. The corresponding fourth order PDE can preserve edges and avoid the staircase effect. The proposed model contains a function of gradient norm as an edge detector, which controls the diffusion speed according to the local structure of the image and preserves more details. Denoising results are given and we have also compared our method with some related PDE models.