We consider a novel variational model for image reconstruction, based on second-order partial differential equations, in this paper. This inpainting approach is inspired by the anisotropic diffusion-based denoising solutions. A stable variational scheme is proposed first. Then, a nonlinear differential model is derived from it, by determining the corresponding Euler–Lagrange equation and applying the steepest descent method. A rigorous mathematical treatment of this anisotropic diffusion scheme is provided next. This nonlinear second order diffusion model is then numerically approximated, a consistent and explicit finite-difference based discretization scheme being developed. Some successful image inpainting experiments and method comparison are also provided in this article. 
Variational image inpainting technique based on nonlinear second-order diffusions