Journal of Advanced Research ( IF 11.4 ) Pub Date : 2020-05-15 , DOI: 10.1016/j.jare.2020.04.015 Antun Lovro Brkić 1 , Darko Mitrović 2 , Andrej Novak 3
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Motivated by the fact that the fractional Laplacean generates a wider choice of the interpolation curves than the Laplacean or bi-Laplacean, we propose a new non-local partial differential equation inspired by the Cahn-Hilliard model for recovering damaged parts of an image. We also note that our model is linear and that the computational costs are lower than those for the standard Cahn-Hilliard equation, while the inpainting results remain of high quality. We develop a numerical scheme for solving the resulting equations and provide an example of inpainting showing the potential of our method.
中文翻译：
从非局部 Cahn-Hilliard 型方程的角度研究图像修复问题。
受分数拉普拉斯算子比拉普拉斯算子或双拉普拉斯算子产生更广泛的插值曲线选择这一事实的启发，我们提出了一种新的非局部偏微分方程，该方程受 Cahn-Hilliard 模型的启发，用于恢复图像的损坏部分。我们还注意到，我们的模型是线性的，计算成本低于标准 Cahn-Hilliard 方程的计算成本，而修复结果保持高质量。我们开发了一个数值方案来求解所得到的方程，并提供了一个显示我们方法潜力的修复示例。
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