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

Charles M. Elliott | Zendy; Beata Gawron | Zendy; S. Maier-Paape | Zendy; Erik S. Van Vleck | Zendy

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

Author(s) -

Charles M. Elliott,

Beata Gawron,

S. Maier-Paape,

Erik S. Van Vleck

Publication year - 2006

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2006.5.181

Subject(s) - smoothing , regular polygon , mathematics , convergence (economics) , scheme (mathematics) , mathematical optimization , convex analysis , convex optimization , mathematical analysis , geometry , statistics , economics , economic growth

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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