Seongjai Kim, Hyeona Lim
Abstract:
Mathematical restoration models, in particular, total variation-based
models can easily lose fine structures during image denoising.
In order to overcome the drawback, this article introduces two
strategies: the non-convex (NC) diffusion and the texture-free residual
(TFR) parameterization.
A non-standard numerical procedure is suggested and its stability
is analyzed to effectively solve the NC diffusion model which is
mathematically unstable.
It has been numerically verified that the resulting algorithm
incorporating the NC diffusion and TFR parameterization is able to not
only reduce the noise satisfactorily but also enhance edges effectively,
at the same time.
Various numerical examples are shown to confirm the claim.
Published February 28, 2007.
Math Subject Classifications: 35K55, 65M06, 65M12.
Key Words: Fine structures; denoising; edge enhancement;
nonphysical dissipation; total variation (TV) model;
non-convex (NC) diffusion model;
texture-free residual (TFR) parameterization.
Show me the PDF file (952K), TEX file, and other files for this article.
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Seongjai Kim Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762-5921, USA email: skim@math.msstate.edu |
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Hyeona Lim Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762-5921, USA email: hlim@math.msstate.edu |
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