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Damped second order flow applied to image denoising
Department of Science and Technology, Linköping University, Linköping, Sweden .
Department of Science and Technology, Linköping University, Linköping, Sweden .
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
Shenzhen MSU-BIT University, 518172 Shenzhen, China; School of Mathematics and Statistics, Beijing Institude of Technology, China.ORCID iD: 0000-0003-4023-6352
2019 (English)In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 84, no 6, p. 1082-1111Article in journal (Refereed) Published
Abstract [en]

In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF.

Place, publisher, year, edition, pages
Oxford University Press, 2019. Vol. 84, no 6, p. 1082-1111
Keywords [en]
Nonlinear flow, image denoising, p-parabolic, p-Laplace, inverse problems, regularization, damped Hamiltonian system, symplectic method, Störmer–Verlet.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-79218DOI: 10.1093/imamat/hxz027ISI: 000509388900002Scopus ID: 2-s2.0-85082102558OAI: oai:DiVA.org:oru-79218DiVA, id: diva2:1386183
Note

Funding Agency:

Alexander von Humboldt Foundation

 

Available from: 2020-01-16 Created: 2020-01-16 Last updated: 2020-04-03Bibliographically approved

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Gulliksson, MårtenZhang, Ye

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