Seongjai Kim, Hyeona Lim
Abstract:
This article concerns mathematical image denoising methods
incorporating fourth-order partial differential equations (PDEs).
We introduce and analyze piecewise planarity conditions (PPCs)
with which unconstrained fourth-order variational models in continuum
converge to a piecewise planar image.
It has been observed that fourth-order variational models holding
PPCs can restore better images than models without PPCs and
second-order models.
Numerical schemes are presented in detail and various examples in image
denoising are provided to verify the claim.
Published April 15, 2009.
Math Subject Classifications: 35K55, 65M06, 65M12.
Key Words: Variational approach; PDE-based restoration model;
fourth-order PDEs; piecewise planarity condition.
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Seongjai Kim Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, USA email: skim@math.msstate.edu |
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Hyeona Lim Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, USA email: hlim@math.msstate.edu |
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