Geodesic
Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
Kybernetika, Tome 43 (2007) no. 6, pp. 777-788.

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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.
Classification : 35B45, 35K57, 35K60, 65M60, 68U10, 74S10, 94A08
Keywords: finite volume method; diamond-cell method; image processing; nonlinear parabolic equation; tensor diffusion 
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     author = {Drbl{\'\i}kov\'a, Olga},
     title = {Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing},
     journal = {Kybernetika},
     pages = {777--788},
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     volume = {43},
     number = {6},
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     zbl = {1140.35362},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a2/}
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Drblíková, Olga. Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing. Kybernetika, Tome 43 (2007) no. 6, pp. 777-788. http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a2/