Existence Theory for the EED Inpainting Problem
Analysis of PDEs
2019-09-18 v2
Abstract
We establish an existence theory for an elliptic boundary value problem in image analysis known as edge-enhancing diffusion (EED) inpainting. The EED inpainting problem aims at restoring missing data in an image as steady state of a nonlinear anisotropic diffusion process where the known data provide Dirichlet boundary conditions. We prove existence of a weak solution by applying the Leray-Schauder Fixed point theorem and show that the set of all possible weak solutions is bounded. Moreover, we demonstrate that under certain conditions, the sequences resulting from iterative application of the operator from the existence theory contain convergent subsequences.
Keywords
Cite
@article{arxiv.1906.04628,
title = {Existence Theory for the EED Inpainting Problem},
author = {Michael Bildhauer and Marcelo Cárdenas and Martin Fuchs and Joachim Weickert},
journal= {arXiv preprint arXiv:1906.04628},
year = {2019}
}