ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Faisal Fairag,
Ke Chen,
Shahbaz Ahmad
S. 108 - 127 doi:10.1553/etna_vol54s108 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol54s108
Abstract: Image denoising using mean curvature leads to the problem of solving a nonlinear fourth-order integro-differential equation. The nonlinear fourth-order term comes from the mean curvature regularization functional. In this paper, we treat this high-order nonlinearity by reducing the nonlinear fourth-order integro-differential equation to a system of first-order equations. Then a cell-centered finite difference scheme is applied to this system. With a lexicographical ordering of the unknowns, the discretization of the mean curvature functional leads to a block pentadiagonal matrix. Our contributions are fourfold: (i) we give a new method for treating the high-order nonlinearity term; (ii) we express the discretization of this term in terms of simple matrices; (iii) we give an analysis for this new method and establish that the error is of first order; and (iv) we verify this theoretical result by illustrating the convergence rates in numerical experiments. Keywords: image denoising, mean curvature, cell-centered finite difference method, numerical analysis Published Online: 2021/01/08 12:01:47 Object Identifier: 0xc1aa5576 0x003c2400 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |