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Relation between total variation and persistence distance and its application in signal processing

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Abstract

In this paper we establish the new notion of persistence distance for discrete signals and study its main properties. The idea of persistence distance is based on recent developments in topological persistence for assessment and simplification of topological features of data sets. Particularly, we establish a close relationship between persistence distance and discrete total variation for finite signals. This relationship allows us to propose a new adaptive denoising method based on persistence that can also be regarded as a nonlinear weighted ROF model. Numerical experiments illustrate the ability of the new persistence based denoising method to preserve significant extrema of the original signal.

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Authors and Affiliations

  1. Institute for Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16-18, 37083, Göttingen, Germany

    Gerlind Plonka & Yi Zheng

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  1. Gerlind Plonka
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  2. Yi Zheng
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Correspondence to Gerlind Plonka.

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Communicated by: Tomas Sauer

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Plonka, G., Zheng, Y. Relation between total variation and persistence distance and its application in signal processing. Adv Comput Math 42, 651–674 (2016). https://doi.org/10.1007/s10444-015-9438-8

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  • DOI: https://doi.org/10.1007/s10444-015-9438-8

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