Please use this identifier to cite or link to this item: doi:10.22028/D291-26313
Title: Theoretical foundations for 1-D shock filtering
Author(s): Welk, Martin
Weickert, Joachim
Galic, Irena
Language: English
Year of Publication: 2005
Free key words: analytical solution
dynamical system
mode filter
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: While shock filters are popular morphological image enhancement methods, no well-posedness theory is available for their corresponding partial differential equations (PDEs). By analysing the dynamical system of ordinary differential equations that results from a space discretisation of a PDE for 1-D shock filtering, we derive an analytical solution and prove well-posedness. We show that the results carry over to the fully discrete case when an explicit time discretisation is applied. Finally we establish an equivalence result between discrete shock filtering and local mode filtering.
Link to this record: urn:nbn:de:bsz:291-scidok-46185
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 150
Date of registration: 24-Feb-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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