Seventh Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 17 (2009), pp. 107-121.

Fourth-order partial differential equations for effective image denoising

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
Hyeona Lim
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
email: hlim@math.msstate.edu

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