Discrete dynamics for convex and non-convex smoothing functionals in PDE based image restoration

C. M. Elliott; B. Gawron; S. Maier-Paape; E. S. Van Vleck

doi:10.3934/cpaa.2006.5.181

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2006, Volume 5, Issue 1: 181-200. Doi: 10.3934/cpaa.2006.5.181

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Discrete dynamics for convex and non-convex smoothing functionals in PDE based image restoration

1.
Department of Mathematics, University of Sussex, Falmer, East Sussex BN1 9QH
2.
Institut für Mathematik, RWTH Aachen, 52062 Aachen
3.
Institut für Mathematik, RWTH Aachen, D-52062 Aachen
4.
Department of Mathematics, University of Kansas, Lawrence, KS 66045

Received: April 30, 2005

Revised: September 30, 2005

Published: February 2006

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Abstract

In this article we consider a model that generalizes the Perona-Malik and the total variation models. We consider discretizations of this new model and show that the discretizations conserve certain properties of the continuous model, in particular convergence of the iterative scheme to a critical point and existence of a discrete Liapunov functional. Computational results are obtained that illustrate different features of the family of models.

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Mathematics Subject Classification: Primary: 35K35, 65M06.

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