Please use this identifier to cite or link to this item: doi:10.22028/D291-26498
Title: Properties of higher order nonlinear diffusion filtering
Author(s): Didas, Stephan
Weickert, Joachim
Burgeth, Bernhard
Language: English
Year of Publication: 2008
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: This paper provides a mathematical analysis of higher order variational methods and nonlinear diffusion filtering for image denoising. Besides the average grey value, it is shown that higher order diffusion filters preserve higher moments of the initial data. While a maximum-minimum principle in general does not hold for higher order filters, we derive stability in the 2-norm in the continuous and discrete setting. Considering the filters in terms of forward and backward diffusion, one can explain how not only the preservation, but also the enhancement of certain features in the given data is possible. Numerical results show the improved denoising capabilities of higher order filtering compared to the classical methods.
Link to this record: urn:nbn:de:bsz:291-scidok-47456
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 215
Date of registration: 5-Jun-2013
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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