Two anisotropic fourth-order partial differential equations for image inpainting

In this study, the authors propose two fourth-order partial differential equations (PDEs) to inpaint the image. By analysing those anisotropic fourth-order PDEs and comparing their diffusion images, the authors confirm they are forward diffusion or backward diffusion. A numerical algorithm is presented using a finite-difference method and analyse the stability of discretisation. Finally, they show various experimental results and conclude that the proposed new models are better than the second-order and third-order PDEs, especially for weakening the blocky effects.