Please use this identifier to cite or link to this item: doi:10.22028/D291-26310
Title: Numerical aspects of TV flow
Author(s): Bürgel, Andrea
Breuß, Michael
Sonar, Thomas
Brox, Thomas
Weickert, Joachim
Language: English
Year of Publication: 2005
Free key words: singular diffusion equation
finite difference methods
numerical stability
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: The singular diffusion equation called total variation (TV) flow plays an important role in image processing and appears to be suitable for reducing oscillations in other types of data. Due to its singularity for zero gradients, numerical discretizations have to be chosen with care. We discuss different ways to implement TV flow numerically, and we show that a number of discrete versions of this equation may introduce oscillations such that the scheme is in general not TV-decreasing. On the other hand, we show that TV flow may act self-stabilising: even if the total variation increases by the filtering process, the resulting oscillations remain bounded by a constant that is proportional to the ratio of mesh widths. For our analysis we restrict ourselves to the one-dimensional setting.
Link to this record: urn:nbn:de:bsz:291-scidok-46160
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 148
Date of registration: 15-Feb-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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