Abstract:An existence theory is developed for an elliptic boundary value problem in image analysis known as edge-enhancing diffusion (EED) inpainting. The EED inpainting problem aims at restoration of missing data in an image as the steady state of a nonlinear anisotropic diffusion process where the known data provide Dirichlet boundary conditions. The existence of a weak solution is established by applying the Leray–Schauder fixed point theorem, and it is shown that the set of all possible weak solutions is bounded. Moreover, it is demonstrated that under certain conditions the sequences resulting from iterative application of the operator from the existence theory contain convergent subsequences.

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中文翻译：

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EED修复问题的存在性理论

摘要：针对图像分析中的椭圆边值问题，提出了一种存在理论，即边缘增强扩散（EED）修补。EED修复问题旨在恢复图像中丢失的数据，作为非线性各向异性扩散过程的稳态，其中已知数据提供Dirichlet边界条件。弱解的存在是通过应用Leray-Schauder不动点定理建立的，并且证明了所有可能的弱解的集合都是有界的。此外，证明了在某些条件下，由存在理论中的算子迭代应用所产生的序列包含会聚子序列。

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