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.
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Communicated by Cristina Turner.
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Rathish Kumar, B.V., Halim, A. A linear fourth-order PDE-based gray-scale image inpainting model. Comp. Appl. Math. 38, 6 (2019). https://doi.org/10.1007/s40314-019-0768-x
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DOI: https://doi.org/10.1007/s40314-019-0768-x