A linear fourth-order PDE-based gray-scale image inpainting model

Abstract

In this paper, we will present a variational PDE-based image inpainting model in which we have used the square of the $$L^2$$ norm of Hessian of the image u as regularization term. The Euler–Lagrange equation will lead us to a fourth-order linear PDE. For time discretization, we have used convexity splitting and the resulting semi-discrete scheme is solved in Fourier domain. Stability analysis for the semi-discrete scheme is carried out. We will demonstrate some numerical results and compare with $$\text {TV}-L^2$$ and $$\text {TV}-H^{-1}$$ model.