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

  • B. V. Rathish KumarEmail author
  • Abdul Halim


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.


Variational approach Inpainting Fourth-order PDE Convexity splitting 

Mathematics Subject Classification

68U10 65K10 65D18 



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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIndian Institute of Technology KanpurKanpurIndia

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