Seventh Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 17 (2009), pp. 107-121. 

Title: Fourth-order partial differential equations for effective
       image denoising

Authors: Seongjai Kim (Mississippi State Univ., MS, USA)
         Hyeona Lim   (Mississippi State Univ., MS, USA)
 
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.