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On a Parabolic-Hyperbolic Filter for Multicolor Image Noise Reduction

Maltsev, Valerii; Pokojovy, Michael

Abstract:
We propose a novel PDE-based anisotropic filter for noise reduction in multicolor images. It is a generalization of Nitzberg & Shiota's (1992) model being a hyperbolic relaxation of the well-known parabolic Perona & Malik's filter (1990). First, we consider a `spatial' molifier-type regularization of our PDE system and exploit the maximal L2-regularity theory for non-autonomous forms to prove a well-posedness result both in weak and strong settings. Again, using the maximal L2-regularity theory and Schauder's fixed point theorem, respective solutions for the original quasilinear problem are obtained and the uniqueness of solutions with a bounded gradient is proved. Finally, the long-time behavior of our model is studied.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000054398
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-543988
KITopen ID: 1000054398
Verlag KIT, Karlsruhe
Umfang 26 S.
Serie CRC 1173 ; 2016/10
Schlagworte image processing, nonlinear partial differential equations, weak solutions, strong solutions, maximal regularity
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