# American Institute of Mathematical Sciences

March  2006, 5(1): 181-200. doi: 10.3934/cpaa.2006.5.181

## 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, United Kingdom 2 Institut für Mathematik, RWTH Aachen, 52062 Aachen, Germany 3 Institut für Mathematik, RWTH Aachen, D-52062 Aachen 4 Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States

Received  May 2005 Revised  October 2005 Published  December 2005

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.
Citation: C. M. Elliott, B. Gawron, S. Maier-Paape, E. S. Van Vleck. Discrete dynamics for convex and non-convex smoothing functionals in PDE based image restoration. Communications on Pure & Applied Analysis, 2006, 5 (1) : 181-200. doi: 10.3934/cpaa.2006.5.181
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