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Title: Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing (English)
Author: Drblíková, Olga
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 6
Year: 2007
Pages: 777-788
Summary lang: English
Category: math
Summary: This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient in normal direction. Moreover, the proofs of $L^2(\Omega )$ – a priori estimates for our discrete solution are given. Finally we present our computational results. (English)
Keyword: finite volume method
Keyword: diamond-cell method
Keyword: image processing
Keyword: nonlinear parabolic equation
Keyword: tensor diffusion
MSC: 35B45
MSC: 35K57
MSC: 35K60
MSC: 65M60
MSC: 68U10
MSC: 74S10
MSC: 94A08
idZBL: Zbl 1140.35362
idMR: MR2388392
Date available: 2009-09-24T20:29:22Z
Last updated: 2013-09-21
Stable URL:
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