Coefficient identification in PDEs applied to image inpainting
2014 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 242, 227-235 p.Article in journal (Refereed) Published
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.
Image inpainting; Inverse problems; Coefficient identification
Mathematics Civil Engineering
IdentifiersURN: urn:nbn:se:liu:diva-110691DOI: 10.1016/j.amc.2014.05.051ISI: 000340563000020OAI: oai:DiVA.org:liu-110691DiVA: diva2:749467