Total Variation Meets Topological Persistence: A First Encounter

Journal Article · Thu Sep 30 00:00:00 EDT 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3497795· OSTI ID:21428569

Bauer, Ulrich; Schoenlieb, Carola-Bibiane; Wardetzky, Max ^[1]

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1. Institut fuer Numerische und Angewandte Mathematik, Lotzestrasse 16-18, D-37083 Goettingen (Germany)

We present first insights into the relation between two popular yet apparently dissimilar approaches to denoising of one dimensional signals, based on (i) total variation (TV) minimization and (ii) ideas from topological persistence. While a close relation between (i) and (ii) might phenomenologically not be unexpected, our work appears to be the first to make this connection precise for one dimensional signals. We provide a link between (i) and (ii) that builds on the equivalence between TV-L{sup 2} regularization and taut strings and leads to a novel and efficient denoising algorithm that is contrast preserving and operates in O(nlogn) time, where n is the size of the input.

• OSTI ID: 21428569
• Journal Information: AIP Conference Proceedings, Vol. 1281, Issue 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3497795; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
FUNCTIONAL ANALYSIS
INTEGRAL EQUATIONS
MINIMIZATION
PARTIAL DIFFERENTIAL EQUATIONS
SIGNALS
TOPOLOGY
VARIATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
MATHEMATICS
OPTIMIZATION