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Coefficient identification in PDEs applied to image inpainting
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-2681-8965
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
2014 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 242, 227-235 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we introduce the concept of parameter identification problems, which are inverse problems, as a methodology to inpainting. More specifically, as a first study in this new direction, we generalize the method of harmonic inpainting by studying an elliptic equation in divergence form where we assume that the diffusion coefficient is unknown. As a first step, this unknown coefficient is determined from the information obtained by the known data in the image. Next, we fill in the region with missing data by solving an elliptic equation in divergence form using this obtained diffusion coefficient. An error analysis shows that this approach is promising and our numerical experiments produces better results than the harmonic inpainting.

Place, publisher, year, edition, pages
Elsevier, 2014. Vol. 242, 227-235 p.
Keyword [en]
Image inpainting; Inverse problems; Coefficient identification
National Category
Mathematics Civil Engineering
URN: urn:nbn:se:liu:diva-110691DOI: 10.1016/j.amc.2014.05.051ISI: 000340563000020OAI: diva2:749467
Available from: 2014-09-24 Created: 2014-09-19 Last updated: 2014-10-14Bibliographically approved

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